Pokemon Red and Blue Versions (Game Boy)

Guide by Paradise1

1) Synopsis / Table of Contents


Set Difficulty	2/10 to beat, 4/10 to master
Approximate time to master	25-30 hours with fast-forward
Minimum numbers of playthroughs needed	1
Number of missable achievements	21
Does difficulty affect achievements?	Not Applicable
Hardest achievement of the set	Gotta Catch 'em All

1) Synopsis / Table of Contents
2) Introduction
3) General Information
4) Walkthrough
Acknowledgements

2) Introduction

Pokemon Red and Blue Version are the Western releases of the first entries in the long-running Pokemon series. Originally released as Pokemon Red and Green in Japan in 1996, an updated version named Pokemon Blue was localized and released in the West in 1998 as the Red and Blue Versions we all know. Despite releasing very late into the Game Boy's lifespan, the games were a smash success, selling over 31 million copies worldwide (to this day, still the best-selling Pokemon games)! They were followed with an anime, a trading card game, and an unbelievable amount of merchandise, launching a multimedia empire that would grow to be the highest-grossing of all time.

Generation 1, as it's known, is beloved by fans for its relatively simple mechanics and classic Pokemon designs. The games hold up decently well today, although various QoL and balance changes made over the years mean that FireRed and LeafGreen may be a better experience if you've never played a Pokemon game before. Still, the games are by no means unplayable, and some even find that the unique mechanics of Generation 1 actually enhance the experience. In fact, this generation has a thriving competitive scene filled with players who love exploring the idiosyncrasies of the Generation 1 battle system.

This set, developed by Blazekickn and dude1286, is quite comprehensive, covering story progression, picking up items, defeating trainers, and, of course, catching 'em all! There are a few frustrating and grindy achievements, but with fast-forward (which I highly recommend) it's honestly not too bad. This was the first set I ever mastered, and I feel like it strikes a good balance difficulty-wise.

This guide doesn't have a beat-by-beat walkthrough, but I've linked a few excellent ones in the Useful Resources section if you'd like. I would also recommend checking out the Achievement Set Tips section for some pointers on the set as a whole. As always, feel free to message me with any suggestions or corrections!

3) General Information

Pokemon Basics

If you've never played Pokemon before, this short video is an excellent introduction to the basic mechanics. Just note that some parts of it don't apply to Generation 1 - namely, Pokemon don't have Abilities, Pokemon can't hold items, and the Special Attack and Special Defense stats are a single stat called Special.

This section will pick up where that video left off and explain some intermediate mechanics of the Pokemon series (and this game specifically) that may prove helpful.

[Keep the Type Chart handy] to figure out what moves are super effective against what types. Note that the type chart has changed over the years, so make sure you're using the one specific to Generation 1.
When a Pokemon uses a move that matches its type (or one of its types, if it has two), it gains a Same-Type Attack Bonus (STAB), which multiplies the move's power by 1.5. This is a very significant boost.
Each Pokemon species has a set of Base Stats that range from 1-255 that determine what its stats will be. For instance, Chansey's base HP is 250, meaning it will have a lot of HP, but its base Attack is 5, meaning it will have a very low Attack stat. This makes certain Pokemon species suitable for certain roles.
- A Pokemon's Base Stat Total (the sum of all five stats) is a good approximation of how powerful they are. For instance, Weedle/Caterpie, the weakest Pokemon in the game, have BSTs of 175, while Mewtwo, the strongest Pokemon in the game, has a BST of 590.
- Typically, when a Pokemon evolves, its Base Stats will go up, making it more powerful.
There are two categories of moves: Physical and Special. Physical moves use the Attack stat of the attacking Pokemon and the Defense stat of the defending Pokemon. Special moves use the Special stat of both the attacking and defending Pokemon. In this generation, whether a move is Physical or Special depends entirely on its type.
- Normal, Fighting, Flying, Poison, Ground, Rock, Bug, and Ghost moves are all Physical.
- Fire, Water, Grass, Electric, Psychic, Ice, and Dragon moves are all Special.
- This means a few Pokemon have a disadvantageous combination of stats and typing. Take the Fire-type Arcanine, for instance - it has an impressive 110 Attack, but if it wants to use Fire-type moves for STAB, it has to use its relatively unimpressive 80 Special.
Whichever Pokemon has the higher Speed stat typically moves first. The only exception are moves that have a different "priority." In Generation 1, the only moves that have different priority are Quick Attack (which moves before all other moves), and Counter (which moves after all other moves). If two opposing Pokemon both use Quick Attack, the one with the higher Speed will move first, as normal.
- In this generation, Speed also affects how often you get a critical hit, doubling your damage. If a speedy Pokemon uses a high crit chance move like Slash, you can basically guarantee a critical hit!
Stat buffs and debuffs have twelve levels, six in each direction. Moves in this game will raise or lower a stat by either 1 or 2 stages. If it says a stat "greatly rose/fell", it's 2 stages, if it just says "rose/fell," it's 1 stage. Once a stat gets to +6 or -6, it can't be boosted higher or lower, respectively. The modifications to stats given by each stage are listed in the table below:

Stage	Multiplier
-6	Stat x .25
-5	Stat x .28
-4	Stat x .33
-3	Stat x .40
-2	Stat x .5
-1	Stat x .66
0	Stat x 1
1	Stat x 1.5
2	Stat x 2
3	Stat x 2.5
4	Stat x 3
5	Stat x 3.5
6	Stat x 4

There are five status effects in the game: Sleep, Paralysis, Burn, Poison, and Freeze.
- Sleep will prevent your Pokemon from moving until it wakes up. It takes a full turn to wake up in this generation, so if you're unlucky, you won't be able to get an attack in at all. Thankfully, sleep-inducing moves are somewhat inaccurate (except for Parasect's Spore).
- Paralysis will cut your Pokemon's Speed to a quarter of its normal value, and the Pokemon will have a 25% chance to not be able to move during a turn. Decreasing Speed also makes it harder to run away from battles. Paralysis doesn't go away naturally - you have to cure it using an item or go to a Pokemon Center. This condition is most often caused by Electric-type moves, but a few other moves can cause it too.
- Burn will cut your Pokemon's Attack in half, and your Pokemon will lose 1/16th of its max HP after every turn. Burn can be cured with items or by healing at a Pokemon Center. This status is caused by Fire-type moves.
- Poison simply decreases the affected Pokemon's HP by 1/16th at the end of each turn. Outside of battle, poisoned Pokemon will take 1 HP of damage for every four steps the player takes. Poison can be cured with items, or by healing at a Pokemon Center. Unsurprisingly, Poison is typically inflicted by Poison-type moves.
- Freeze prevents Pokemon from moving at all. In this generation, Pokemon will never unfreeze by themselves - they either have to be hit with a Fire-type move, or healed using items or a Pokemon Center. Thankfully, Freeze is relatively rare - it's only caused by Ice Beam and Blizzard, each with only a 10% chance of freezing the opponent.
If your Pokemon's stats are debuffed, you can restore them by switching out to a different Pokemon and switching back. This will also cure confusion, but will have no effect on status conditions like paralysis, sleep, freeze, or poison (with one exception)
- The exception is bad poison, caused by the move Toxic. Bad poison will increase the damage it does every turn (from 1/16th to 2/16ths to 3/16ths, and so on), but it can be converted to regular poison by switching out.
Status effects are very helpful in catching Pokemon, especially in this generation. Getting a Pokemon that learns Thunder Wave early (like Pikachu), will be a great help.
PP restoring items like Ethers and Elixers cannot be bought. Be careful about using them, as you may want to keep a few to make some achievements a little easier.

Generation 1 Differences

A more exhaustive list can be found on this page. I'll note some of the more applicable differences here.
Perhaps the most major difference is the Special stat. In this game, Pokemon have a single Special stat which acts both as their attack stat when using Special moves, and as their defense stat against Special moves. This makes Pokemon with high Special absolutely busted.
Speaking of Special moves, moves in this game are Physical or Special based only on their type. Normal, Fighting, Flying, Poison, Ground, Rock, Bug, and Ghost moves are all Physical. Fire, Water, Grass, Electric, Psychic, Ice, and Dragon moves are all Special.
TMs in this game are single-use. Be careful about who you give them to.
Although there is a Pokemon Day Care south of Cerulean City, you can only put one Pokemon in there and can't breed Pokemon.
Pokemon cannot hold items.
Pokemon do not have abilities.
Item space is severely limited in this generation. In my opinion, this is the most annoying part about playing these games. Your Bag has space for 20 stacks of items (up to 99 items in each stack without glitches), and your PC has room for 50 more. This isn't enough room for every possible item, so you'll have to choose what to prioritize. For TMs, I would definitely recommend keeping TM03 (Swords Dance), TM13 (Ice Beam), TM24 (Thunderbolt), TM26 (Earthquake) and TM29 (Psychic) until the end of the game, as these are strong attacks that will be very useful for the Elite Four achievements. If you're playing Red version, MAKE SURE you keep TM16 (Pay Day), as the Wario Would Be Proud achievement is otherwise very annoying to get (or missable, even). Otherwise, feel free to use or sell/toss TMs as you prefer.
If your Pokemon Box is full, you won't be able to catch additional Pokemon unless you head back to the PC and switch it yourself.
Some type interactions are different. Consult The Generation 1 Type Chart for details. Most notable are probably Poison being super effective to Bug (and vice versa, for whatever reason), and Ghost being completely ineffective against Psychic.
The balance between types is infamously lopsided in these games. In general, Psychic and Normal are very good due to their type matchups, strong attacks, and Pokemon with excellent stats. Many types which seem good on paper, such as Bug, Fighting, Ghost, and Dragon, have few good damaging moves, making them not very useful offensively. Ultimately, the game is easy enough to which you can make pretty much anything work, though, so don't be too discouraged.
Critical hits are based on Speed, not a fixed ratio. They deal approximately twice as much damage as a normal hit. They also ignore all stat changes of both the defender and the attacker, positive and negative, meaning that if a Pokemon's Attack is boosted enough, a non-critical hit can do more damage than a critical hit.
It takes one full turn to wake up from Sleep in this generation - the Pokemon won't attack on the same turn.
Freeze will never go away naturally in this generation. It can only be removed with items, being hit by a Fire-type move, or Haze.
There is no move reminder in this game, so if you overwrite a move, it's gone forever.
There's also no move deleter, which means that any HM moves you teach to a Pokemon cannot be overwritten by any means.
If you level up a Pokemon more than one level in one go, any moves learned on levels you skipped will not be learned.
If you attack a dual-type Pokemon with a move that one of its types is weak to and the other type resists, (e.g. hitting a Normal/Flying type with a Fighting move), the game will falsely state that the move is either super effective or not very effective instead of neutral. The actual damage calculation is unchanged, though. See this article for more specifics.
Finally, and perhaps most infamously, due to a programming error, every move has a 1/256 chance to miss, even if it's 100% accurate. This is known as a "Gen 1 Miss." The only exceptions are Swift and using an X Accuracy, which both allow you to bypass the bugged accuracy check entirely.

Red or Blue?

Although this set is doable in either version, Blue has a few quirks that make it slightly better in my opinion.
The Game Corner prizes are slightly different in each version, and for whatever reason, buying all Pokemon (required for an achievement) costs about 5000 coins less in Blue than in Red (15670 vs 20179, to be precise).
The Wario Would Be Proud achievement is missable in Red, as Meowth is only available in Blue, and you can discard/overwrite the Pay Day TM. If you're careful, this won't be a problem, but it's something you don't have to worry about if you're playing Blue.
Scyther is slightly harder to catch in the Safari Zone than Pinsir, making the Have Fun achievement slightly harder.
I think the version-exclusive Pokemon in Blue are slightly more viable, strictly speaking.
All that being said, none of these are a complete deal-breaker, so feel free to play whichever version you prefer.

Glitches

Pokemon Red and Blue are absolutely riddled with glitches. Several of these can be used to the player's advantage, such as the item duplication glitch which can let you obtain basically infinite money. Feel free to use these glitches if you'd like (it's not against the RetroAchievements rules), but I'll be writing this guide assuming that you won't be using any glitches. Not intentionally, at least. I also can't guarantee that achievements will work properly if you use glitches, so use them at your own risk.
Be careful catching any Pokemon you're not "supposed" to have (i.e. other starters, other eeveelutions)! See the Gotta Catch 'em All guide in Catch 'em All Achievements for more details.

Achievement Set Tips

You're going to want to spread out your XP a little bit to stay under the level cap for the gym leader achievements. You'll need to keep up with obtaining and evolving Pokemon anyway for the Oak's Aide achievements, so try and level up different Pokemon as you go!
You're definitely going to want to pick up every item and fight every trainer as you go. Nothing is more devastating than getting to the end and realizing you missed a single item or trainer somewhere. The Bulbapedia and zerokid guides linked in the next section have lists of items obtainable per area. The StrategyWiki guide and zerokid guide also have labeled maps (although not all of the StrategyWiki maps are labeled). Fabio Attard's checklist linked in the next section can also be very helpful for keeping track if you want to be methodical about it.
Once you jump down from Route 4 into Cerulean City, you won't be able to go back to Pewter or Viridian City until a little later in the game. Make sure you have everything you need for Misty's achievement beforehand.
You should pick a Pokemon in the early or midgame to be an "EV friend" for the Where's My Ribbon? achievement. Full details on Stat EXP are in the Adventure Achievements section, but the short version is that if you use a Pokemon you go through the whole game with, you won't need to grind as much at the end. I would recommend either your starter, Nidoking/Nidoqueen, Snorlax, Eevee, or Lapras.
- Whenever you get a Vitamin (HP Up, Protein, Iron, Calcium, Carbos), you should use them all on your EV Friend. Using the Vitamins will give you a good head start on maxing out a Pokemon's Stat Exp, but there's a maximum you can get to with Vitamins, so it's better to use them sooner rather than later. Plus, it saves bag space!
- Eventually, you're going to want a Pokemon who can solo the Elite 4, both for the Elite Stomp achievement and for grinding levels to evolve Pokemon for the Pokedex. This will also award lots of Stat EXP as well, so it might as well be your EV Friend. Saving good coverage TMs (Ice Beam, Thunderbolt, Earthquake, Psychic, etc.) for this point will make this easier.
In the comments of the Gym Leader challenge achievements, people seem to report having trouble unlocking them fairly often. To figure out why, I looked into the achievement code myself, and found (to the best of my knowledge) the three conditions that will prevent you from earning the achievements:
- If Shift Mode is on, it will prevent you from earning the achievement. You can turn Shift Mode into Set Mode in the in-game Options menu.
- While the gym music is playing (i.e. before the battle), if any Pokemon is above the level cap, if will prevent you from earning the achievement. Even if you don't use them in the battle, it will prevent you from earning it. However, if a Pokemon levels up beyond the cap during the battle, it won't prevent you from earning the achievement, despite what the forum post says.
- During the fight, if you open the item menu and press A FOR ANY REASON (even to hit cancel), it will prevent you from earning the achievement.
After you complete the Pokemon Tower, the game actually opens up quite a bit, and you can actually do Gyms out of order. In this guide, I've routed Silph Co. and Sabrina before Koga, as that's the route the Bulbapedia and StrategyWiki guides (linked below) follow. Feel free to do Koga first if you'd like! Just remember that the level cap is 43 for both of them, and that there's a missable achievement in the Safari Zone.

Useful Resources

Bulbapedia is the most thorough and accessible source of Pokemon information out there. You can use it for Pokemon locations, learnsets, item locations, and more. Note that by default pages display information and movesets for the latest generation, which definitely won't be accurate for Generation 1. Usually there will be a button to view different generations, if applicable.
The Serebii Generation 1 Pokedex has thorough information on all Pokemon specific to Generation 1, and without extra information on things like the anime. If you want a more streamlined and Gen 1-specific experience than Bulbapedia, this is likely your best bet.
The Generation 1 Type Chart is worth keeping handy. There are several notable differences from later generations.
GitHub user Fabio Attard has created a checklist of all event flags in the game that is an absolute godsend for keeping track of all sorts of things for this run (Items, trainers, trades, gift Pokemon, etc.). If you feel like it would be helpful, feel free to print it out or paste it into a document and check off as you go. I'll be using sections of his checklist for the "collect all items in an area" achievements.
Smogon has a guide for all hidden items with pictures included. Very handy! I'll also use these images as appropriate.
Bulbapedia and StrategyWiki both have an excellent beat-by-beat walkthrough if you'd like to follow them. They also provide a list of items and trainers in each area to keep on top of those achievements. Bulbapedia lists the items in a single easy-to-parse box, while StrategyWiki tends to include them throughout the text, and has labeled maps for many areas. Choose which style you prefer. Bulbapedia also has the advantage of being specific to Red and Blue, whereas StrategyWiki includes Yellow, which may be slightly more confusing.
This GameFAQs guide by zerokid is also excellent, and additionally provides in-depth explanations of Gen 1 mechanics and glitches, and viability rankings for each Pokemon. It also has labeled maps for every area, which is excellent for keeping track of items and trainers.
The Cave of Dragonflies is a treasure trove of really in-depth information on Gen 1 mechanics, as well as every other generation. Of particular interest for this set are the Gen 1 Catch Rate Calculator and the Gen 1 Safari Zone Calculator.

4) Walkthrough

Step 1: Story

In this section, we'll be going over the story of the game and grabbing missable achievements along the way. This part is separated into subsections by badge. Around the midpoint of the game, you can actually do things in a few different orders. I've decided to route Silph Co. and Sabrina's Marsh Badge before the Soul Badge, as that's what a few guides recommend. This might make it tough to find a specific achievement if it's not where you expect, so I would recommend using Ctrl-F to search for the achievement name.

In terms of missable achievements, the most common ones are for defeating Gym Leaders on Set Mode without items within a certain level cap. See the Achievement Set Tips for more specific details.

MISSABLE ACHIEVEMENTS:

Step 2: Elite 4 / Postgame

There are a few achievements for defeating the Elite 4 in special ways, so I'll group them in this section. If you kept at least a few great TMs, you should have no problem crafting teams to get through these conditions fairly easily. If not, there's no shortage of cheesy tactics you can use, so don't worry.

The only truly missable achievements in this section are for capturing Mewtwo without the Master Ball. You may want to keep Smogon in mind too, though, as you can definitely make that achievement harder than it needs to be if you don't prepare accordingly.

MISSABLE ACHIEVEMENTS

Step 3: Catch 'em All/Miscellaneous

This Section will have multiple subsections. The first, Adventure Achievements, will detail achievements for collecting items, defeating Trainers, leveling Pokemon, and other miscellaneous things you may do while exploring the Kanto region. Catch 'em All Achievements will naturally have to do with completing your Pokedex. Game Corner Achievements cover winning and buying prizes at the Celadon Game Corner. Safari Zone Achievements cover the two achievements for catching Pokemon in the Safari Zone. Finally, Battle Achievements cover the achievements earned from fulfilling certain conditions in battle.

MISSABLE ACHIEVEMENTS

Uno, Dos, Tres!
Gotta Catch 'em All
Wario Would Be Proud (missable in Red Version)

Step 1: Story | Total points: 336

Boulder Badge

As you begin the game, pick your starter. Bulbasaur is probably the easiest, as it makes the first two gyms easier, but pick whoever you choose. After you fight Blue for the first time, go ahead and head north to Viridian City. Whatever you do, DO NOT buy any Poke Balls or catch any Pokemon, as that will lock you out of our first missable achievement.

Free Points (1)
Obtain a free sample courtesy of the Viridian City Pokemon Mart.

As you head north to Viridian City, talk to the first person on your left to grab a free Potion.

Journey Has Started (5)
Obtain the Pokedex.

Grab Oak's Parcel from the Poke Mart in Viridian and bring it back, and Oak will give you the Pokedex.

The United Cities of Kanto (2)
Obtain a map of the region.

After getting the Pokedex, head to Blue's house north of the lab and his sister will give you the Town Map. After that, start training for the next rival fight, but remember - don't catch any Pokemon or buy any Poke Balls!

Parting Gift (5)
Obtain 5 Poke Balls from Prof. Oak.

MISSABLE

In order to get Poke Balls from Oak, you'll have to defeat your rival on Route 22 west of Viridian City without buying Poke Balls and therefore without catching any additional Pokemon. Blue brings a level 9 Pidgey and a level 8 starter. Pidgey can be annoying to deal with, as it will use Sand-Attack and lower your accuracy, and you can't switch to a different Pokemon to restore your stats. If you're using Bulbasaur, Leech Seed can help give you an edge, as it will do passive damage even with lower accuracy. For Squirtle and Charmander, you can try and use STAB (same-type attack bonus) attacks like Bubble or Ember. For the starter, just use Tackle/Scratch (and Leech Seed with Bulbasaur) and hope for the best. I managed to get through at Level 10 with some luck, but you might need to go a bit higher. Just keep in mind that Brock has a Level 14 cap, and you also can't evolve your starter, as that would count as having captured another Pokemon.

Once you defeat Blue, go ahead and return to Oak, who will give you a few Poke Balls and remind you what the point of the game actually is. After that, feel free to start catching Pokemon and filling up your team! Make sure you keep your starter at level 12 or 13 if you plan to use them during the Brock fight. At this point, you may want to catch 2 extra NidoranMs and an extra Spearow for in game trades later on, but you can save that for later too if you'd like.

(Thanks to MagicalChef1007, tinycyan, alcoatjez, lo9i, and others in the comments for their suggestions!)

Setting the Forest Ablaze (5)
Find every Item and defeat every Trainer in Viridian Forest.

HIDDEN ITEM – Viridian Forest – Antidote

FIELD ITEM – Viridian Forest – Poké Ball
TRAINER BATTLE – Viridian Forest – Bug Catcher (Rick)
TRAINER BATTLE – Viridian Forest – Bug Catcher (Doug)
FIELD ITEM – Viridian Forest – Antidote
FIELD ITEM – Viridian Forest – Potion
HIDDEN ITEM – Viridian Forest – Potion

TRAINER BATTLE – Viridian Forest – Bug Catcher (Sammy)

Anybody Home? (5)
Go from one entrance of Viridian Forest to the other without initiating any wild encounters. (No resetting, no Repel or Cut)

You don't have to get this on the first try, so if you run into a Pokemon, exit the forest and try again.

From Bulbapedia:

Basically, what you'll want to do, coming from the north side, is to walk through as few grass tiles as possible until you can take the white path the rest of the way. Starting from the north side lets you reset quicker if you run into an encounter.

Defeat Brock (5)
Earn the Boulder Badge in Pewter City.

Rock Smash (5)
Defeat Brock on Set Mode without using items in battle. (Level 14 Cap)

MISSABLE

If you picked Squirtle or Bulbasaur, this battle is very easy. Brock has just two Pokemon: a level 12 Geodude, and a level 14 Onix. Both are 4x weak to Grass and Water. Bulbasaur learns Vine Whip at level 13, and Squirtle learns Bubble at level 8. If you picked Charmander, you might have a harder time. The best option is probably to evolve a Caterpie into a Butterfree and have it learn Confusion at Level 12. Geodude and Onix have pretty low Special, so any type of Special attack will take them out pretty easily.

Cascade Badge

Make sure to buy the Magikarp in Mt. Moon Pokemon Center - it's considered to be a "gift" Pokemon (and at only 500 Pokedollars, it practically is a gift!).

Shoot for the Moon (5)
Find every Item and defeat every Trainer in Mt. Moon.

TRAINER BATTLE – Mt. Moon B2F – Team Rocket Grunt
TRAINER BATTLE – Mt. Moon B2F – Team Rocket Grunt
HIDDEN ITEM – Mt. Moon B2F – Moon Stone

TRAINER BATTLE – Mt. Moon B2F – Super Nerd (Miguel)

Make sure you keep the Moon Stones you get in here. There are only five in the game, and you'll need to use them on four different Pokemon to complete the Pokedex (Those being Nidorino, Nidorina, Jigglypuff, and Clefairy).

Only Take One (5)
Choose a Fossil at the end of Mt. Moon.

You can take whichever you want. You won't be able to revive them until much later in the story, so it probably doesn't matter too much, but I think Omastar is better, strictly speaking.

Again, once you jump down into Cerulean City, you won't be able to return to Pewter or Viridian City (unless you death-warp to the last Pokemon Center you used), so make sure you're ready to take Misty down!

Defeat Misty (5)
Earn the Cascade Badge in Cerulean City.

Pool's Closed (5)
Defeat Misty on Set Mode without using items in battle. (Level 21 Cap)

MISSABLE

Misty has a level 18 Staryu and a Level 21 Starmie. Starmie is probably the biggest threat we've faced so far, as it has quite high stats, especially Special and Speed. If you have an Ivysaur, Misty probably won't give you too much trouble. If not, here are some suggestions:

A Pikachu from Viridian Forest, (assuming you caught one) would probably be your best bet. As supersharpy64 and Vespidcrown note in the comments, you can try and land a Thunder Wave to paralyze Starmie to prevent it from outspeeding all of your Pokemon, allowing them to finish the KO if Pikachu goes down.
You could also use one of the Moon Stones you picked up in Mt. Moon to get an early Nidoking evolution. Nidoking has very good stats for this part of the game. However, his Ground typing leaves him weak to Water moves, so you might have to bring something else to finish the job,
Magikarp evolves at level 20, and Gyarados' massive 125 Attack stat combined with its Water resistance will take down Starmie without too much trouble.
If all else fails, you can grab a Spearow and/or Rattata from Route 4 and evolve them at level 20. Raticate's Hyper Fang will put in work.
If you're playing Red version, you could even try and cheese with Ekans' wrap (assuming Starmie is paralyzed, so you outspeed it), which will slowly but surely get you the win.
Another cheesy strategy would be to use Pidgeotto's (or Sandshrew's) Sand-attack to lower Starmie's accuracy, as Slackot suggests in the comments.

Thunder Badge

After defeating Misty, there's not much else to do in Cerulean right now. There's a trainer wanting to trade Poliwhirl for Jynx, but we can't quite get a Poliwhirl yet, so that will have to wait. Head north to Route 24, defeating Blue and the trainers on the Nugget Bridge. On Route 24, you may want to catch an extra Abra if you can for an in-game trade later. Once you rescue Bill, return to Cerulean City and head south on Route 5 to get to Vermilion City. In the north gate of the Underground path, there's a girl offering a NidoranF for a NidoranM. Not the most exciting deal, but it's required for an achievement, so go ahead and do it if you have an extra NidoranM.

Once you get to Vermilion City, there's another trade available - Farfetch'd for Spearow. Go ahead and do it if you have a Spearow you're willing to part with. Farfetch'd is not very strong, but makes a decent HM friend, as it can use Cut and Fly. In any case, both the trade and Farfetch'd are required for achievements. If you want to catch an extra Spearow, the closest place is Route 4, west of Cerulean.

You'll also want to grab the Old Rod and the Bike Voucher while you're here.

I Like To Ride It (5)
Obtain the Bicycle from the Bike Shop in Cerulean City.

Once you get the Bike Voucher by listening to the old man in the Pokemon Fan Club north of the Vermilion Gym, you can head back to Cerulean City and obtain the Bike. There's no pressing need, though, so you can do it later if you'd like.

Once you're ready, head to the S.S. Anne. Note that once you get the HM01 Cut from the Captain and then leave the ship, it will sail off, never to return. This makes a few achievements missable, so make sure you don't pick up Cut until you're ready! Before you pick up Cut, you can enter and exit the ship as many times as you'd like, though.

Also keep in mind that Lt. Surge's level cap is only 24, so make sure you're spreading experience out (or be ready to leave some Pokemon in the PC).

Sleeping Giant (2)
Be told about a legendary Pokemon that sleeps a lot.

MISSABLE

The man who tells you about Snorlax is located on the second floor, in the leftmost cabin.

My Heart Will Go On (10)
Collect all optional Items and defeat all optional Trainers on the S.S. Anne.

MISSABLE

TRAINER BATTLE – S.S. Anne B1F – [Missable] Fisherman (Barny)
TRAINER BATTLE – S.S. Anne B1F – [Missable] Sailor (Phillip)
HIDDEN ITEM – S.S. Anne B1F – [Missable] Hyper Potion

TRAINER BATTLE – S.S. Anne Deck – [Missable] Sailor (Trevor)
TRAINER BATTLE – S.S. Anne Deck – [Missable] Sailor (Edmond)
TRAINER BATTLE – S.S. Anne 2F – [Missable] Fisherman (Dale)
TRAINER BATTLE – S.S. Anne 2F – [Missable] Gentleman (Brooks)
FIELD ITEM – S.S. Anne 2F – [Missable] Max Ether
TRAINER BATTLE – S.S. Anne 2F – [Missable] Gentleman (Lamar)
TRAINER BATTLE – S.S. Anne 2F – [Missable] Lass (Dawn)
FIELD ITEM – S.S. Anne 2F – [Missable] Rare Candy

Make sure you get all of them before you get HM01 Cut!

A Boatload of Fun (5)
Rub the Captain's Back on the S.S. Anne and obtain HM01 Cut.

Once you get Cut, make sure that you have picked up all the items and battled all the trainers you need to. The S.S. Anne will depart as soon as you exit.

Be careful about teaching Cut - in this game, HMs cannot be overwritten by any means, so it's probably best to designate 1 Pokemon as an HM friend (like Farfetch'd) so you don't have to put Cut on your stronger Pokemon.

Cut opens up a lot for us, but since we're in Vermilion, let's go ahead and challenge Lt. Surge's gym first.

Defeat Lt. Surge (5)
Earn the Thunder Badge in Vermillion City.

One Man Army (5)
Defeat Lt. Surge on Set Mode without using items in battle. (Level 24 Cap)

MISSABLE

Lt. Surge has a level 21 Voltorb, level 18 Pikachu, and level 24 Raichu. Raichu in particular is a threat with it's Thunderbolt and high Special. Here are a few strategies to get by.

As blood and Dragonskhan mention in the comments, Ground types will completely wall Raichu. If you need one, you can head east of Vermilion to Diglett's Cave to grab a Diglett. You can also find level ~30 Dugtrio, but they are above the level cap. Watch out for Screech from Voltorb and Quick Attack from Pikachu, though. If you have 2 Ground Pokemon, you should be in the clear.
Ivysaur (and other Grass types) resists Electric moves (Bulbasaur fans stay winning), allowing you to whittle down the first two Pokemon.

Rainbow Badge

After defeating Surge, head east to Route 11.

Lawn Mower (2)
Cut the grass.

Wherever there's tall grass, you can use Cut to clear a patch of it, allowing you to (very tediously) walk risk-free through a route. Probably not all that useful, but it's a neat feature!

Metal Detector (5)
Obtain the Itemfinder from the Aide on Route 11.

The Aide is found on the second floor of the gate on the east side of route 11. If you have caught 30 types of Pokemon, he'll give you the Itemfinder. Next to him is a guy who will trade Nidorina for Nidorino. Again, unimpressive, but it's required.

You can't head east any more because Snorlax is blocking the way, so head through Diglett's Cave back to Route 2. South of the exit onto Route 2 is a house where a kid will offer his Mr. Mime for an Abra. This is the only way to get Mr. Mime, so trade an Abra if you have an extra one.

Flashing Lights Warning (5)
Obtain HM05 Flash from the Aide on Route 2.

Further south, there's another gate where an Aide will give you HM05 Flash if you've caught at least 10 types of Pokemon. Again, HMs can't be overwritten in this game, so be careful about who you teach it to.

After getting Flash, there aren't any achievements until you reach Celadon City. You can use Cut to get TM42 (Dream Eater) in Viridian City and the Old Amber from the Pewter Museum on the way.

Once you reach Celadon, you can pick up Eevee through the back door of the Pokemon Mansion, visit the Department Store (make sure to get an extra drink for the guard and at least 2 Poke Dolls), and challenge Erika at the Celadon Gym.

Defeat Erika (5)
Earn the Rainbow Badge in Celadon City.

Kicking Some Grass (10)
Defeat Erika on Set Mode without using items in battle. (Level 29 Cap)

Erika has a level 29 Victreebell, a level 24 Tangela, and a Level 29 Vileplume. Victreebell and Vileplume are probably the biggest threats - they can put you to sleep with Sleep Powder, which really sucks in Gen 1. Here's some suggestions:

Charmander users finally get their first W (and Bulbasaur boys their first L). Charmeleon should have no problem ripping through Erika's Pokemon.
You can also grab a Growlithe/Vulpix on Route 8 east of Saffron City or Route 7 east of Celadon.
Kadabra will make short work of Victreebell and Vileplume due to their Poison typing. Kadabra learns Psybeam at level 27, and should outspeed to avoid Sleep Powder if your level is high enough.
You can use your Flash Pokemon to lower the accuracy of Sleep Powder even further if you'd like.

After defeating Erika, we'll have to go tackle the Rocket Hideout and the Pokemon Tower.

Marsh Badge

The Rocket Hideout is located within the Celadon Game Corner. You could try a few of the Game Corner achievements, or you could wait until later when you have more funds.

Raiding the Vault (5)
Find every Item and defeat every Trainer in the Rocket Hideout.

TRAINER BATTLE – Rocket Hideout B1F – Team Rocket Grunt
FIELD ITEM – Rocket Hideout B1F – Escape Rope
TRAINER BATTLE – Rocket Hideout B1F – Team Rocket Grunt
HIDDEN ITEM – Rocket Hideout B1F – PP Up

Ghost Buster (5)
Obtain the Silph Scope from the Rocket Hideout.

Now that you've gone to all that effort to get the Silph Scope, go ahead and put it (and the Lift Key) into your PC so you can get an achievement in the Pokemon Tower. Before you head back to Lavender Town, take a short detour to the west, onto Route 16. This will allow you to grab Fly, which will be very useful.

Prepare For Liftoff (5)
Obtain HM02 Fly from the secret house on Route 16.

Snorlax will be blocking the entrance to Route 16 proper, but you can Cut a tree to go through the northern path instead. Doing so, you'll find a house with a woman who will give you the Fly HM! If you brought an HM friend like Farfetch'd, you can teach it to them now, and Fly straight to Lavender Town. Otherwise, you can walk back to Celadon and go east, potentially unlocking the gates to Saffron City by giving the guards a drink item.

Grave Robbing (5)
Find every Item and defeat every Trainer in the Pokemon Tower.

Dearly Beloved (5)
Gift the forced Ghost encounter at the top of Lavender Tower a Poke Doll to calm it without using the Silph Scope.

MISSABLE

If you encounter the Ghost at the top without a Silph Scope in your inventory, you can use the Poke Doll item to end the fight. Due to a programming oversight, this counts as defeating the Ghost, allowing you to progress!

GHOST!? (5)
Save Mr. Fuji and obtain the Poke Flute.

After getting to the top floor and rescuing Mr. Fuji, make sure you talk to him so he'll give you the Poke Flute. If you'd like, you can go back into the Pokemon Tower with the Silph Scope to catch Gastly and Cubone.

At this point, you actually have a few options. For your next badge, you could challenge Silph Co. and Sabrina in Saffron City or Koga in Fuchsia City. The level cap for both gyms is 43, so there's a lot of room to train Pokemon up. I'll be following the order in the Bulbapedia and Strategy Wiki guides, which both do Sabrina first.

When you get to Saffron, there's not much you can do, as Team Rocket has taken control of the city. Our ultimate goal is Silph Co., but if you want, you can challenge the Fighting Dojo beforehand.

Enter the Dragon (5)
Claim your prize from the Saffron City Dojo.

The Dojo is the building that says GYM right next to the regular gym. You'll face five Black Belts, who all have fighting-type Pokemon. A Psychic type like Kadabra will make short work of them. Once you defeat them, you can choose Hitmonchan or Hitmonlee. Hitmonlee is probably slightly better, as the elemental punches that Hitmonchan learns are Special attacks, and Hitmonchan's Special is an unimpressive 35.

Next, we'll fight through Silph Co. Make sure you save before you enter, as there's a missable achievement that requires you to "sneak" your way through.

Ekans Dilos (5)
Reach the Rival in Silph Co. without defeating more than 1 trainer.

Here are step-by-step instructions, adapted from MarvellousDazza's guide in the comments:

Enter the front door, and head straight to the elevator at the back. Head up to the 5th floor.
Walk left until you see two plant pots. Head south of them to avoid a Trainer to the west, and then follow the hallway south to the bottom.
There should be a Rocket Grunt standing next to a teleport pad. This is our one mandatory encounter - defeat him, then use the teleporter pad. Teleport back the way you came, and you should be able to folllow the hallway south and east to grab the Card Key.
Once you grab the Card Key, open the door to the northeast of the Rocket Grunt you just defeated. Inside that door, to the south of the boxes, is another teleporter. Take that one.
Follow the hallway east and turn north as soon as you're able to. There will be a door on the west side of the hallway - go through that door, and step on the teleporter, and the fight with Blue should start, giving you the achievement!

Once you earn this achievement, do note that you'll have to go back and battle all the trainers you missed before you fight Giovanni in order to get the next achievement.

Hostage Situation (25)
Find every Item, defeat every Trainer, and open all Doors in Silph Co.

MISSABLE

Note that the Trainers will disappear once you defeat Giovanni. As Grahamtams says in the comments, Giovanni will challenge you immediately when you walk through his door, so make sure that you've gotten everything before you do! The Blue fight, picking up Lapras, the Giovanni fight, and the Master Ball don't count towards this achievement, so it should pop as soon as you open the last door to Giovanni.

Biggest Balls In Kanto (5)
Obtain the Master Ball from the President of Silph Co.

After you're done, a few things open up - you can use a Poke Doll to get TM31 Mimic, and you can challenge Sabrina's gym.

Defeat Sabrina (10)
Earn the Marsh Badge in Saffron City.

Brawn Over Brains (10)
Defeat Sabrina on Set Mode without using items in battle. (Level 43 Cap)

MISSABLE

Sabrina can be tough, as Psychic has no good counter in this game. What's more, Kadabra and Alakazam often like to use Recover, wiping out any progress you may have made. Enemies don't have PP in this game, so they can use Recover indefinitely. Here's a few suggestions:

As NimbusSpark suggests, Snorlax is a good option. You can catch one using the Poke Flute (detailed in the next section). Snorlax comes knowing Amnesia, which boosts Special by two stages. After KOing Kadabra, Snorlax can buff up its defenses with Amnesia, and then take down the rest of the Pokemon using Body Slam (learned at level 35), exploiting their relatively weak physical defense.
Raichu, Jolteon, or Electrode could use Thunder Wave to paralyze Alakazam, lessening the chance that it will successfully use Recover.
As rickyplays suggests, you can grab a Dugtrio from Diglett's Cave and use Dig.
Dragon Rage (from Gyarados or Charizard) is still a decent option for guaranteed damage.
If all else fails, you can use Double Team to cheese the fight. TM32 Double Team is buyable at the Department Store, and can be taught to almost every Pokemon in the game (Metapod fans in shambles). Mr. Mime is a decent Pokemon to set up on.

Monkey's Tounge (5)
Navigate through the Saffron City Gym using the fewest amount of warps. (Start from Gym Entrance)

You don't need to do this on the first try - you can come back after you defeat Sabrina.

As several users state, the solution is (after taking the first warp) to take the northwest portal, the southwest portal, and the southwest portal again.

After you defeat Sabrina, get ready to head down to Fuchsia City.

Soul Badge

There are a couple ways to get to Fuchsia City. West of Celadon City is Cycling Road, spanning Routes 16, 17, and 18. This Route is quick to travers, has a bunch of hidden items, and a trade (Slowbro for Lickitung) on Route 18. I don't think you could have a Slowbro yet, but you'll need to come back when you do.

Meanwhile, south of Lavender Town are Routes 12, 13, 14, and 15. These routes have a long gauntlet of Trainers, which takes longer, but you can get a bunch of XP. Route 12 also contains a house with the Super Rod. Choose whichever way you prefer. Or choose both!

The Sleeper Awakens (5)
Use the Pokeflute to awaken and catch Snorlax.

MISSABLE

Whichever way you go, a sleeping Snorlax will be blocking the way. Use the Poke Flute to awaken them, and then battle and catch them.

Note that if you KO Snorlax, it won't respawn, which is what makes this achievement missable. Thankfully, there are two Snorlaxes, so if you miss one, you can try and catch the other. I would still recommend saving beforehand though, just to be safe.

Snorlax is a very good Pokemon in Gen 1. With its high Attack, it can use Normal-type STAB moves like Body Slam, Double-Edge, and Hyper Beam very effectively. Its Special of 65 is just OK, but with access to Amnesia, which boosts Special by 2 stages, Snorlax can become very tanky, and even dish out some major Special damage of its own with moves like Surf.

In the gate from Route 15 east of Fuchsia City, you can grab two achievements:

Sharing is Caring (5)
Obtain an Exp. All from the Aide in Fuchsia City.

Oak's Aide can be found on the second floor of the gate. If you've caught 50 species of Pokemon, you can get the EXP. All, an item that splits EXP evenly between different Pokemon in your party while it's in your bag. This can be useful for making sure your Pokemon stay under a level cap, or for leveling up multiple species of Pokemon to evolve them.

Unidentified Flying Object (2)
Glance at a mysterious bird in the distance using the binoculars.

Also on the second floor of the gate are two pairs of binoculars. One of them will show a bird flying in the distance, and will bring up a picture of Articuno.

You can still get this even after you've caught Articuno - the bird will still appear in the binoculars.

Once you enter Fuchsia City proper, you can either head straight for the Gym or do some exploring first.

Froggy! (5)
Obtain all 3 Fishing Rods.

If you got the Old Rod in Vermilion City and the Super Rod from the house on Route 12, then you can get this achievement by getting the Good Rod from the house directly to the east of the Warden's.

Defeat Koga (10)
Earn the Soul Badge in Fuchsia City.

Ninja Gaiden (10)
Defeat Koga on Set Mode without using items in battle. (Level 43 Cap)

After Sabrina, Koga's not so bad. All four of his Pokemon are pure Poison type, so a Psychic type Pokemon can rip him to shreds. The only potentially annoying things are his Muk using Minimize, or his Weezing using Selfdestruct (although at that point you've already won). Here are some tips:

Kadabra is perfect for this challenge, especially since it learns the incredibly powerful Psychic at level 38. It will likely be able to outspeed and one-shot all of Koga's Pokemon, avoiding the Minimize issue from Muk.
A Ground Pokemon can be good, using either Dig or Earthquake. Graveler learns Earthquake at level 36, and Diglett learns it at level 40 (if you delay the evolution). You can also use the Earthquake TM you got in Silph Co., but you may want to hang onto it until the Elite 4 instead (or be careful about who you give it to).
Snorlax learns the powerful move Body Slam at level 35, and is a decent option. If you get unlucky, Muk might stack more than one Minimize, though.

Ace of the Maze (5)
Navigate through the Fuchsia City Gym without bonking. (Start from Gym Entrance)

This one isn't missable - you can retry by exiting the Gym and entering again. If you look closely, you can see the pattern of the invisible walls on the floor, so it shouldn't be too hard to avoid. As Earthsouls and Sebta mention, hitting walls, trainers, and the edge of the map will void the achievement. Basically, if you hear the "bonk" sound, it voids the achievement. As Vespidcrown suggests, go slowly and tap the button to go one space at a time if you need to.

Volcano Badge

Before entering the Safari Zone, empty out your bag so that you have at least 12 open slots. There are ten optional items you'll need to collect in one run, and two quest items. You need Surf to get one of the items, so you may want to get Surf on the first trip and get the rest on a subsequent trip. If you have a good route, you can get all of them in one trip assuming you've beaten Koga and bring a Pokemon who can learn Surf. You can see an example in this video by OmegaVideoGameGod.

Too Much Water (5)
Obtain HM03 Surf from the Safari Zone.

Surf is found in a house in the western area. You'll have to loop around through the east and northern areas to get there, though. While you're there, you can also pick up the Gold Teeth if you'd like but don't pick up any other items, as you'll need to get the rest in one visit. If you want, with the rest of your time you can try fishing for Magikarp with the Old Rod for Getting Your Money's Worth (see the Safari Zone Achievements).

No Item Left Behind (10)
Collect all optional Items in the Safari Zone in a single Safari Hunt. (No resetting)

Make sure you save before entering the Safari Zone, and that you have space in your bag for all the items.

There are ten optional items in the Safari Zone. Try to take them area by area. zerokid's guide has excellent maps of each area.

FIELD ITEM – Safari Zone Center – Nugget
FIELD ITEM – Safari Zone East – Carbos
FIELD ITEM – Safari Zone East – Max Potion
FIELD ITEM – Safari Zone East – TM37 (Egg Bomb)
FIELD ITEM – Safari Zone East – Full Restore
FIELD ITEM – Safari Zone North – TM40 (Skull Bash)
FIELD ITEM – Safari Zone North – Protein
FIELD ITEM – Safari Zone West – TM32 (Double Team)
HIDDEN ITEM – Safari Zone West – Revive

FIELD ITEM – Safari Zone West – Max Potion
FIELD ITEM – Safari Zone West – Max Revive

Performance Enhancement Disk (5)
Obtain HM04 Strength from the Safari Zone Warden in Fuchsia City.

After your adventure in the Safari Zone, give the Gold Teeth to the Warden in his house east of the Pokemon Center. He'll give you the HM04 Strength in return. Make sure you grab the item that's nearby!

Slowpoke is a decent choice for a second HM Friend - it can learn Strength, Surf, and Flash. You can grab one in the Safari Zone (if you're not sick of it yet), or a higher-leveled one in the Seafoam Islands coming up.

Now that you have Surf, you can either head on to the Seafoam Islands, or you can backtrack to the Power Plant on Route 10, east of Cerulean City. In both locations you can capture a legendary bird Pokemon - Articuno and Zapdos, respectively. The easiest way to catch legendary Pokemon in this game is to inflict them with a status and chuck Ultra Balls. Sleep is ideal, but even Paralysis gives a ~10% catch chance at full HP. Don't worry too much about trying to get them to low HP - the increase to catch chance is pretty marginal compared to inflicting them with a status. Alternatively, you could use the Master Ball on one of them, as we won't be using it for Mewtwo. Whatever you do, make sure you save before you battle them - if you KO them, they won't come back!

If you do end up going to the Power Plant, make sure you battle and defeat (or catch) the Voltorbs and Electrodes disguised as items - clearing them all is required for an achievement.

Finally, you may want to keep Articuno and Zapdos in the box for now. Not only are they above the level cap, but them coming at level 50 makes them ideal as a Plan B (or Plan A) for the Smogon achievement (which also has a level cap of 50).

Cinnabar Island has a bunch of things to do. First of all, you can head to the Pokemon Lab, which contains a scientist who can revive your fossil Pokemon! If you've received every other gift Pokemon so far, the It's Present achievement should pop. The lab also contains our final three in-game trades for No ~Multi~ Set Required. The three trades are Venonat for Tangela, Raichu for Electrode, and Ponyta for Seel. Venonat can be caught in a lot of places, and Ponyta can be caught in the Pokemon Mansion here on Cinnabar Island. If you don't want to evolve your own Raichu, you can find wild Raichu in Cerulean Cave in the postgame, and in the Power Plant in Blue version (in place of Electabuzz). Full details for these two achievements are located in Adventure Achievements.

Once you're ready, head into the Pokemon Mansion.

GB Bungaku Zenshuu (5)
Read all Journals in the Cinnabar Mansion without leaving. (No resetting)

There are two journals on the second floor, one on the third floor, and one in the basement.

Once you finish the Pokemon Mansion, make sure you save before you enter the gym - unlike Sabrina and Koga, there is a MISSABLE gym achievement!

2000 IQ Super Quiz (5)
Complete all of the Quizzes in the Cinnabar Island Gym without leaving the building, fighting any trainers, or resetting.

MISSABLE

You'll need to get all of the quiz answers correct in one go. Don't save in between them - if you accidentally get one wrong, reload your save from before the Gym!

MarvellousDazza shares the answers:

Yes (as IanJ1988 notes, this is debatably incorrect, as Caterpie evolves into Metapod, not Butterfree)
No
No
No
Yes
No

Once you answer the sixth question, the achievement will pop. At this point, you can go back and talk to the trainers to challenge them if you'd like. They're not required for any achievements, though, so you can just go ahead and fight Blaine if you'd like.

Defeat Blaine (10)
Earn the Volcano Badge at Cinnabar Island.

Fire Fighter (10)
Defeat Blaine on Set Mode without using items in battle. (Level 47 Cap)

Blaine has four Pokemon: a level 42 Growlithe, a level 40 Ponyta, a level 42 Rapidash, and a level 47 Arcanine. All are pure Fire-types, so their weakness should be easy to exploit:

To be honest, basically any Water type with Surf can take Blaine down. I managed to do it with a level 38 Slowbro without setting up at all. You can easily catch a suitable Pokemon in Seafoam islands.
Surf is pretty widely teachable, so even Pokemon like Snorlax or Nidoking can get in on the action. Just remember that you can't overwrite it.
Ground and Rock type Pokemon are also an option. Earthquake will easily take down Blaine's team.

Earth Badge

There's not much else to do at this point besides heading back to Viridian City to challenge the final Gym Leader. Either Surf north from Cinnabar to return to Pallet Town, or Fly straight to Viridian, and get ready for our final Gym Challenge.

Defeat Giovanni (10)
Earn the Earth Badge in Viridian City.

Blasting Off Again (10)
Defeat Giovanni on Set Mode without using items in battle. (Level 50 Cap)

Giovanni brings a level 45 Rhyhorn, a level 42 Dugtrio, a level 44 Nidoqueen, a level 45 Nidoking, and a level 50 Rhydon. Here are some tips:

Water Pokemon are again likely your best bet. Surf will wreck Giovanni's team, especially Rhyhorn and Rhydon who are 4x weak to it.
Grass Pokemon like Venusaur aren't too bad either, although they may struggle against Nidoking and Nidoqueen due to their Poison typing.
As always, Kadabra is a great choice, especially for Nidoqueen and Nidoking who are weak to Psychic type attacks.

From StrategyWiki:

One Of A Kind (2)
Grab the only Item Ball in the game that is inside of a Gym.

There is a Revive tucked in a hallway to the right of the central area, as shown in the picture above.

Spin to Not Win (5)
Navigate through the Viridian City Gym without using the Spin Tiles. (Start from Gym Entrance)

To do this, you'll have to go through the central area, past Trainer 4 and Trainer 5. Note that Trainer 5 will block your path, so you'll need to exit the Gym and enter again to reset him. This achievement isn't missable - you can get it after defeating the gym.

Victory Road

We're in the home stretch! Head west of Viridian City to battle your Rival one more time and then head up to Victory Road.

If you can, try and keep a few Pokemon below Level 50 for the Smogon achievement. Conveniently, the legendary birds come at Level 50, so if you keep them in the Box for now, that serves as a decent backup plan if one of your Pokemon goes over.

Victory Lap (10)
Find every Item and defeat every Trainer in Victory Road.

Note that if you're playing Red and don't have TM16 Pay Day (because you overwrote/discarded it), the female Cooltrainer on 1F and the Tamer on 2F both have Persians that know Pay Day. If you've defeated all other trainers and haven't earned Wario Would Be Proud yet, this is your last chance to earn it before you'll need to start a new save file.

FIELD ITEM – Victory Road 2F – Guard Spec.
HIDDEN ITEM – Victory Road 2F – Full Restore

TRAINER BATTLE – Victory Road 3F – Cooltrainer♂ (George)
FIELD ITEM – Victory Road 3F – TM47 (Explosion)
TRAINER BATTLE – Victory Road 3F – Cooltrainer♀ (Caroline)
FIELD ITEM – Victory Road 3F – Max Revive
TRAINER BATTLE – Victory Road 3F – Cooltrainer♂ (Colby)
TRAINER BATTLE – Victory Road 3F – Cooltrainer♀ (Alexa)

You can also find Moltres on 2F to complete the Uno, Dos, Tres! achievement.

Once you reach the Indigo Plateau, take a minute to take stock of your Pokemon and remaining TMs to build a team for the Elite 4 achievements.

Step 2: Elite 4/Postgame| Total points: 95

Elite 4

Pokemon Master! (25)
Beat the Elite Four and the Champion of the Pokemon League.

There are five Elite Four achievements - one for just beating them, and four for beating them under specific conditions. The latter four you can overlap without too much trouble, or you can tackle them individually to make it easier. I'll go through each one individually.

If you've been saving your TMs, now's the time to use them. Having a wide variety of moves on one Pokemon (like having Ice Beam/Thunderbolt/Psychic/Surf on a single Pokemon) will be incredibly helpful for coverage and versatility, especially for Elite Stomp.

I'll also be theorizing a worst-case scenario for each achievement, which will attempt to build a team from scratch without using any non-infinite TMs, missable Pokemon, or non-buyable items like Ethers. Expect plenty of cheese. This is mostly for fun, but feel free to take some inspiration if you've run out of TMs or leveled your good Pokemon past the level cap.

I would recommend you tackle Smogon first due to the lower level cap.

Smogon (10)
Defeat the Pokemon League using Set Mode without using items in Battle. (Level 50 Cap, No resetting starting from entering door)

You should save before you enter the door in case you fal and need to try again.

As the achievement description suggests, the level 50 requirement only applies when you enter the door. Once you're past, you're free to level up your Pokemon past 50 either through battling or, as Slumbo mentions, spamming Rare Candies (although you might want to save them for Elite Stomp)

Also, make sure you don't save in the middle - you need to do it all in one go, so you'll need to start from the beginning if you fail.

You can (and should) use items in between the fights - bring Full Heals, healing items (I like Fresh Water), and Revives. You might want to save at least some Ethers and Elixers for later, if you can.

There are many great recommendations in the achievement comments. You can either head in with a well-rounded team as AlveenKamfort suggests, or go in with one overwhelming Pokemon as Kiwiron or Merricid suggest. I myself managed to get through with a team of Slowbro, Jolteon, Snorlax, Kadabra, Nidoking, and Articuno, all at level 38-44 (except for Articuno). If you're looking for a Pokemon to add, sticking Double Team (buyable in the Department Store) on Articuno and/or Zapdos is a good choice - Articuno comes with Ice Beam and has a fantastic 125 Special. If you level Articuno to 51, it will learn Blizzard, too, which is busted in Gen 1 (90% accuracy?!). It might be tempting to use the Thunderbolt TM on Zapdos, but I think it's better suited for giving coverage to a Pokemon for the next achievement, Elite Stomp.

WORST CASE SCENARIO

This is probably the hardest one to do under the worst case scenario. The game is very stingy with good moves (Not a single Pokemon learns Thunderbolt by level up? Seriously?), you can't cheese with items, and many Pokemon that may be good are either missable (Snorlax, Articuno, Nidoking) or dependent on TMs (Chansey, Tauros)
Double Team (TM32) is your best friend. It is buyable at the Celadon Department Store, and is compatible with almost every Pokemon in the game. If you manage to get 6 up, the opponent will only have a 25% chance to hit (using a 100% accurate move)
Water-type Pokemon are a good choice due to their compatibility with Surf, a free and very powerful Water-type move.
- Slowbro is a good answer for Bruno, as it can use Amnesia after setting up Double Teams to greatly boost Surf's damage
- Cloyster is probably your answer for Lance - it learns the excellent move Ice Beam at exactly Level 50, and can be evolved right away using a Water Stone.
Dugtrio learns Earthquake at level 47 and is very fast, providing an answer to Agatha's Poison type Pokemon.
Kadabra is a must-have - the powerful move Psychic can hit most Pokemon for neutral damage and Poison and Fighting type Pokemon for super-effective damage. With Double Team and Recover, it can also survive pretty well. You might even want two of them, to be honest.
Dodrio is a good option - it has 110 Attack, Drill Peck is the strongest Flying move in the game (maybe good for Blue's Exeggutor), and STAB Take Down and Hyper Beam (via TM) are decent options. STAB Tri Attack is also good, although do note it doesn't inflict status conditions in this generation.
- If Hyper Beam KOs a Pokemon in this game, it doesn't take a turn to recharge.
- Fearow is another decent option, but is outclassed by Dodrio in pretty much every way.
- Tauros is also a decent option for STAB Hyper Beam and Take Down (and Strength, I guess), and is a bit bulkier than Dodrio due to its higher base HP, Defense, and Special. Tauros is less versatile, though, and has a slightly lower Attack (100 vs Dodrio's 110).
Lorelei might be tough to deal with. No Electric Pokemon learn Thunderbolt by level-up, leaving most with either the weak Thunder Shock or the inaccurate Thunder. Red players have Electabuzz, who learns Thunder Punch. Blue players can level up Pikachu to 43 before evolving for Thunder.
- Alternatively, there's a pretty infamous exploit you can use. If you send out a Pokemon weak to Psychic, Lorelei's first Dewgong will attempt to use Rest against it endlessly (as it thinks it's a super effective attack). You can use this time to setup your Pokemon. For instance, Machoke can set up with Double Team and then Use Low Kick or Karate Chop to take down Lorelei's Pokemon.
Electrode learns no Electric moves via levelup, but does learn Explosion at level 47. Could be useful as a tactical nuke for a problematic Pokemon like Alakazam or Exeggutor.

If you create a balanced level 50 team, abuse Double Team, and get a little lucky, it should be possible to get through.

Elite Stomp (10)
Beat the Pokemon League with only one Pokemon in your party. (No resetting starting from entering door, No Mew or Mewtwo)

This one is decently easy to combine with Prof. Perfect - if you do it with a Pokemon who's less than level 60, you'll unlock both at the same time.

The ability to use items makes this significantly easier. You can buff your Pokemon up with X items, heal any damage they may have taken, and then unleash high-damage attacks to easily win. To make it easy, load up a single Pokemon with great TMs like Thunderbolt, Ice Beam, Psychic, Earthquake, Surf, or Flamethrower so you have a super-effective option against nearly every Pokemon. The Ice Beam/Thunderbolt combo alone hits everything for at least neutral damage, and hits many Pokemon for super-effective damage. If you have an EV friend you've been training for Where's My Ribbon?, you might want to choose them if they're compatible so that they can gain EVs while soloing the Elite 4 to level up other Pokemon.

I myself got through with only a level 42 Starmie with Surf/Thunderbolt/Ice Beam/Psychic (similar to MisterJay in the comments). I tested it a few times, and while you need to use a lot of X Specials at lower levels, as you approach level 60, you don't need to use any at all.

There is no level cap to this achievement, though. You'll likely be grinding the Elite 4 to level up Pokemon to evolve them for the Pokedex (and to max out Stat EXP), so you can come back after a bit of grinding too make it easier on yourself.

WORST-CASE SCENARIO

Being able to use items makes this one relatively easy. I think if you took a Level 60 Slowbro, taught it Surf, Strength, Psychic (Level 55) and Double Team, and loaded it up with X Attacks and X Specials, you could get through just fine.

Prof. Perfect (10)
Defeat the Pokemon League without having any Pokemon faint. (Level 60 Cap, No resetting starting from entering door)

As stated above, it's not too difficult to combine this with Elite Stomp. But if you want to do it separately, it's even easier. You can use Switch mode to swap out injured Pokemon and exploit the weakness of the incoming Pokemon (especially for Blue), and you can use healing items and X items to increase the survivability and destructive potential of any Pokemon.

WORST-CASE SCENARIO

Again, being able to use items makes this pretty easy. If you buff up a Pokemon with X items, you should be able to survive anything and hit back hard.

Brand Loyalty (10)
Defeat the Pokemon League using a full party of version exclusive Pokemon. (No resetting starting from entering door)

As the achievement says, you'll need to do this with a full party. You don't need to have 6 different Pokemon, though, so you can bring multiple Pokemon of a single species if you'd like. Items are fair game, and there's no level cap. Here's some notes on all the options:

RED

Electabuzz might be your best option. If you have it learn Thunder Shock, Thunder Punch, and Thunder, you should be good to go if you use X items copiously. As cykette suggests, you can use an X accuracy to make Thunder always hit.
Arcanine isn't quite as good as Ninetales in this generation, as Fire-type moves are all Special. Still, it can put some work in. As WKGames notes, though, you'll have to level Growlithe up to level 50 before evolving if you want it to learn Flamethrower (which you probably do).
Vileplume has a good 100 Special, but is probably not incredibly useful in the Lorelei or Blue fights due to the Ice and Psychic-type Pokemon. Vileplume's Grass-type attacks will also be ineffective against most of Agatha and Lance's Pokemon. What's more, there aren't too many good Grass-type moves to begin with. You're probably going to want to level Gloom up to level 38 for Petal Dance (or 52 for SolarBeam).
Scyther is fast and hits hard, but learns absolutely zero STAB moves in R/B. Still, it makes a good backup. If you're going to use Slash, don't bother with X Attacks, as attack boosts don't factor into critical hits in this generation.
Primeape is a decent physical attacker, and may be useful as a backup. Submission is probably its best option for Fighting-type STAB, so don't make it your primary attacker.
Arbok is not great. although it can learn Fissure by TM to try and cheese fights using X Speeds and an X Accuracy.

BLUE

Ninetales is pretty fantastic. Vulpix learns Flamethrower at level 35, and you can catch them at level 34 in the Pokemon Mansion. PP is somewhat limited, though, so you'll either have to bring Ethers, rely on different moves, or rely on different Pokemon.
Pinsir learns the OHKO move Guillotine at level 30, and as FrozenFirebird suggests, you can use X Accuracy and X Speed to cheese most of the fights.
Sandslash can learn Fissure by TM to cheese fights as well. Otherwise, it can definitely get by using physical attacks like Slash, but when you factor in STAB, Persian might be the better choice for that. Remember, if you're using Slash, don't bother using X Attacks, as attack boosts don't affect critical hits in this gen! You can also teach it Earthquake by TM if you don't have a better use for it.
Persian's Normal typing makes it hit hard with STAB Normal moves like Slash, and its high Speed makes it quite likely to land critical hits. If you're using a lot of X Items, though, that might actually be a downside, as critical hits don't take stat boosts into account.
Magmar is not bad - its access to Fire Punch as well as Flamethrower lessens the PP concerns that Ninetales has, and its decent 95 Attack means it can put in work with moves like Strength.
Victreebell is in much the same boat as Vileplume - it has a respectable 100 Special, but its typing isn't well-suited for several fights. Victreebell does have the advantage of learning Razor Leaf (if you level Weepinbell up to 38), which is probably the best Grass move in the game.

WORST-CASE SCENARIO

With no level cap and items available for use, this isn't too bad. You could grind one Pokemon up to a high level to try and sweep (just make sure you remember to fill the rest of your party), or you can grind a few up to have more coverage. And remember, Double Team and X Item spam is always an option.

Cerulean Cave

After defeating the Elite 4, get ready to head to Cerulean Cave. You're going to want to stock up on Ultra Balls (probably at least 50-60), and bring a Parasect or two (for Spore), and/or a Pokemon with Thunder Wave. You'll also probably want to bring plenty of Revives, healing items, and Max Repels. Finally, MAKE SURE you switch to an empty PC Box before you go into the cave.

Area Unknown (10)
Catch every Normal Wild Encounter Pokemon in Cerulean Cave without leaving the area. (No Reseting, No Master Ball)

For this achievement, you'll have to catch all 15 of the cave encounters (i.e. not surfing or fishing) in Cerulean Cave without leaving the cave. This also doesn't include Mewtwo. User tomojin has created an excellent checklist, reproduced here slightly altered to include Sandslash, as Jonny8567 notes:

1F (Entrance area)

2F (Maze area)

B1F (Mewtwo's area)

The bolded entries represent the floor with the highest odds to encounter each individual Pokemon. In order to catch each Pokemon, the easiest way is, as cykette suggests, to inflict them with a status (preferably sleep, but paralysis or poison will do) and then chuck Ultra Balls. You can lower their HP too if you'd like, but putting a Pokemon to sleep will give you at least a 20-40% chance (depending on the species) to catch them with an Ultra Ball even at full HP. Paralysis and Poison are slightly weaker, but still give a respectable 10-30% chance with an Ultra Ball.

Parasect is probably a good choice to put Pokemon to sleep, as its Spore move is 100% accurate. Parasect is slow, though, so it will likely have to take a hit before getting Spore off. If you need a high-leveled Parasect, you can catch one right here in Cerulean Cave, and optionally return to the Pokemon Center to refresh it. Spore also only has 15 PP, meaning you may need to bring Ethers, another Parasect, or a Pokemon that can use Thunder Wave.

As several users note, Electrode might be your biggest problem. Electrode is very fast, can't be paralyzed by Thunder Wave, and has the moves Selfdestruct and Explosion, which gives it a 50% chance every turn to blow up and severely damage your Pokemon. You might want to try catching it sooner rather than later, so it doesn't ruin your run. You can either take the 50% chance and try to get a Spore off, or, as thecoimbra states, you can just try and throw balls. In this case, it's actually better to throw Great Balls (this is what Chickenzes27 is alluding to), as they have a higher catch rate for Pokemon at full HP without a status condition (If they do have a condition, Ultra Balls are better). A Great Ball has about a 15% chance to catch an Electrode at full health.

As JungleCrew states, you can use Repels to easily encounter Ditto on 2F (the maze area) by putting a level 60 Pokemon at the front of your party. Alternatively, you can use Repels and a level 53/54 Pokemon on 2F to only encounter Chansey, Ditto, and Wigglytuff, who may be somewhat difficult to find otherwise.

The Strongest Pokemon Ever! (10)
Catch the fabled Mewtwo.

A Fair Fight (10)
Catch Mewtwo without using the Master Ball.

MISSABLE

Mewtwo, the strongest Pokemon in the game, is found on B1F of Cerulean Cave. Make sure you save before you challenge it! To catch it without the Master Ball, you should follow the same strategy we've been using for legendaries so far: inflict a status condition, and then throw Ultra Balls. Use Spore to put Mewtwo to sleep if Parasect can survive a turn, otherwise use Thunder Wave to paralyze Mewtwo. If Mewtwo is asleep, there's a 21.6% chance to catch it per Ultra Ball thrown, and if it's paralyzed, there's an 11.5% chance to catch it. Don't bother trying to take Mewtwo's HP down, as this will only provide a few extra percent to the catch rate (and it knows Recover, anyways).

Once you've completed Cerulean Cave, you have access to all the Trainers and Items for Genocide Routeand Living Itemfinder, respectively. Remember, there's a Lass west from Cerulean Cave that's easy to miss!

Now that you've finished all the story content in the game, it's time to finish up any miscellaneous achievements you may have left. After that, prepare for the final grind of leveling up Pokemon to evolve them for Gotta Catch 'em All, and to grind Stat EXP for Where's My Ribbon?. If you have been training an EV friend, use them to sweep the Pokemon League to level up Pokemon, so you don't have to grind as much at the end.

Step 3: Catch 'em All/Miscellaneous | Total points: 354

Adventure Achievements

It's Present (5)
Claim all 6 Gift Pokemon. (Including Revived Fossils and Magikarp)

As Jayzor notes, the 6 Gift Pokemon are:

The Magikarp from the Salesman in the Mt. Moon Pokecenter (stretching the definition of the word "gift").
Eevee from the Celadon Mansion (enter through the back).
Lapras from a Silph Co employee in the same room as the Rival Battle.
Hitmonchan or Hitmonlee, from the Saffron City Dojo.
Omanyte/Kabuto from the fossil you got at the end of Mt. Moon, revived in the lab on Cinnabar Island.
Aerodactyl, from the Old Amber you can get from the Pewter City Museum. Revived in the lab on Cinnabar Island.

No ~Multi~ Set Required (5)
Complete all 9 in-game trades.

The 9 trades are:

Abra for MARCEL the Mr. Mime on the east side of Route 2 north of Viridian City.
NidoranM for SPOT the NidoranF in the Route 5 Underground Pass terminal south of Cerulean Cty
Nidorino for TERRY the Nidorina in the east gate on Route 11 east of Vermilion City
Slowbro for MARC the Lickitung in the gate on the west side of Route 18 west of Fuchsia City
Poliwhirl for LOLA the Jynx in the house west of the Pokemon Center in Cerulean City.
Spearow for DUX the Farfetch'd in a house southeast of the Pokemon Center in Vermilion City
Raichu for DORIS the Electrode in the Pokemon Lab on Cinnabar Island
Venonat for CRINKLES the Tangela in the Pokemon Lab on Cinnabar Island
Ponyta for SAILOR the Seel in the Pokemon Lab on Cinnabar Island

Lickitung, Mr. Mime, Jynx, and Farfetch'd can only be acquired via trade in this game. Also, traded Pokemon will earn experience at a boosted rate (1.5x)! This may not be too useful for our purposes, though, as we're trying to stay below level caps.

Now It Is 100 Percent Safe (10)
Find and clear all of the stationary Pokemon in Kanto.

As rhas777 notes, you don't necessarily have to capture all of the Pokemon, just defeat them. The 15 Pokemon are:

The ghost Marowak in Pokemon Tower
The two Snorlaxes on Route 12 south of Lavender Town and Route 16 west of Celadon City.
The 8 Voltorbs/Electrodes disguised as items in the Power Plant
Zapdos in the Power Plant
Articuno in the Seafoam Islands
Moltres in Victory Road
Mewtwo in Cerulean Cave

Disk Collector I (25)
Find all 50 not missable TMs and HMs on the overworld.

List of all TMs and HMs in Red and Blue

This achievement includes all TMs and HMs on the above list except for the two on the S.S. Anne (TM08 Body Slam and TM44 Rest), and the three bought from the Rocket Game Corner (TM15 Hyper Beam, TM23 Dragon Rage, and TM50 Substitute). The TMs sold at the Department Store also have a spawn in the overworld - you must collect them, buying them won't count for this achievement!

Note that this achievement works by detecting if you've received them, not whether they're in your inventory. So feel free to use or sell/toss them once you've acquired them. It's probably impossible to keep them all, anyway.

Many of the comments have suggestions of easy-to-miss TMs, so check them out if you can't figure out which one you're missing!

Living Itemfinder (25)
Find all not missable items (including hidden items) on the overworld.

If you've been keeping up on getting items by following a guide, this shouldn't be too much trouble. But it can be tough if you're missing one or two items and have no idea where they might be. If you're in that situation, the first thing I might recommend is to take a look and make sure you have the achievements for collecting all items in Viridian Forest, Mt. Moon, the Game Corner, the Rocket Hideout, the Pokemon Tower, Silph Co., the Viridian City Gym , and Victory Road. If you have all those achievements, that means you can at least rule out checking those areas (assuming you didn't get those achievements and then reset without saving for whatever reason). And if you don't have those achievements, then that's a good place to start looking. Note that it might be a Trainer that you're missing, and if you don't have the Silph Co. achievement, you can't battle any of the Trainers.

Note that you don't need to worry about items on the S.S. Anne, as those are considered missable.

The second thing I would recommend is to go through the list of hidden items. Hidden items are easy to miss, so you might want to go through each one methodically to make sure you have them all. You might want to try using the Itemfinder while doing this, as for some items it's easy to check a slightly wrong spot and check it off your list without actually getting it.

The final thing I recommend is to read through the achievement comments for frequently-missed items. They include the Rare Candy in the Warden's house in Fuchsia City, the hidden Nugget in the Copycat's house in Saffron City, and the hidden items on Cycling Road. As Farzeer suggests, using the Itemfinder on Cycling Road is very helpful, as it can be a little difficult to figure out precisely where the hidden items are. Also, a lot of people seem to miss items in Viridian Forest, apparently due to resetting after getting the achievement. It might be worth checking out just to be sure.

You can use this checklist along with a guide to methodically go through every item if you'd like.

(Thanks to many in the comments for their suggestions, including but not limited to Marvincenzi, Mophmeister, Baitos, DryIce53, ddot, Farzeer, mooMoony, and itschriz)

Genocide Route (50)
Defeat all not missable Trainers in the Kanto region.

Again, if you've been keeping up by following a guide, this shouldn't be too much trouble. This achievement doesn't include missable trainers, including:

Gym trainers (including the Fighting Dojo)
Trainers on the S.S. Anne
Trainers in Silph Co.
The Team Rocket grunt that gives you the Nugget on Nugget Bridge (missable if you lose to him)

The achievement also doesn't seem to include story battles such as Gym leaders, Rival fights, or Giovanni fights. Also, despite what some users say in the comments, stationary encounters like the legendary birds do not count towards this achievement.

Like the item achievement above, if you're missing a trainer, the first thing I would suggest is to make sure you have all the achievements for defeating all trainers in Viridian Forest, Mt. Moon, the Rocket Hideout, the Pokemon Tower , and Victory Road. Assuming you didn't get these achievements and then reset, you can safely rule these areas out. If you don't have one of these achievements, that's a good place to start looking (although it may be an item you're missing instead).

After that, take a look at the achievement comments for some commonly-missed trainers. The water routes especially have some that are easy to miss. Other potential spots are the Lass west of Cerulean Cave, Cycling Road, and the maze on Route 13 east of Fuchsia City. Note that some comments are outdated - for instance, the achievement was updated to not require the Fighting Dojo trainers. It may have required the legendary birds at some point too, but does not anymore.

You can use this checklist along with a guide to methodically go through every trainer if you'd like.

(Thanks to several users in the comments for their suggestions, including but not limited to Crims0nScorpion, Mophmeister, DryIce53, MissingNoL, WKGames, Jungon, Gutter, AppleAndo, tomojin, and PhazePrime)

Preparing To Be The Very Best (5)
Assemble a full team of Pokemon.

All you need to do is have six Pokemon in your party. You'll likely get this one without even trying.

Anti-Darwinism (2)
Prevent your Pokemon from evolving.

If you press the B button when a Pokemon is evolving, it will stop the evolution. Note that this may prevent it from learning a move, so it's probably best to do it on a Pokemon you don't care too much about.

Halfway (Solo) (5)
Get the Pokemon in Slot 1 from Level 49 to Level 50.

You'll likely do this naturally when facing the Elite Four, or while grinding Pokemon for the Pokedex. Just make sure the Pokemon is at the front of your party.

Halfway (Party) (10)
Level a Pokemon from Lvl 49 to Lvl 50 in a party of Lvl 50+ Pokemon.

If you didn't get this naturally, you can catch a bunch of level 50+ Pokemon in Cerulean Cave and then level up a single Pokemon from 49 to 50.

Where's My Ribbon? (25)
Max out a Pokemon's Stat Experience. (Hint: Try Cerulean Cave!)

You're likely going to want to save this for last. You'll naturally grind Stat EXP while doing other things like leveling up Pokemon for Pokedex completion, so you might as well do all of that first so you can spend as little time grinding as possible.

I'm about to go in-depth on how Stat EXP works, but if you're just interested in the easiest way to get the achievement, here it is: Feed a Pokemon vitamins (HP Up, Protein, Iron, Calcium, and Carbos) until it won't take any more (should be 10 of each if you're starting from scratch), and then either challenge the Pokemon League or defeat wild Pokemon in Cerulean Cave until the achievement pops.

So what is Stat EXP, anyways? This article describes it in full detail, but the gist of it is that each of the 5 stats has an experience value, between 0 and 65535. Whenever you defeat a Pokemon, its base stats will be added to the experience of each stat. For instance, defeating a Pidgey will grant 40 HP experience, 45 Attack experience, 40 Defense experience, 35 Special experience, and 56 Speed experience. These values will be split up if multiple Pokemon take part in a battle, similar to normal experience. This also applies to the Exp. All!

The boost that Stat EXP gives (at level 100) is given by the following formula:

$$\frac{\sqrt{Stat EXP}}{4}$$

It maxes out at 63 additional points. Your Pokemon's stats will gain their bonuses from Stat EXP either upon level up, or if you put the Pokemon in the PC and take them out again. The second method is the only way to update your Pokemon's stats if it's at level 100.

Vitamins will give a Pokemon 2560 experience in a stat. However, you can't use them to increase past 25600 experience, meaning it's best to use them sooner rather than later. If you try to give a vitamin to a Pokemon who's above 25600, the game won't let you, so don't worry about wasting them. Vitamins can be bough for 9800 Pokedollars at the Celadon Department Store, meaning you'll need 490,000 Pokedollars if you want to buy 10 of each. HP Up will increase HP (imagine that), Protein will increase Attack, Iron will increase Defense, Calcium will increase Special, and Carbos will increase Speed.

Unlike later generations, there's no picking and choosing which stats you want to prioritize - you can (and will) max out every stat!

In order to grind effectively, you'll have to face Pokemon with high base stats, which means we're mostly looking for fully-evolved Pokemon. The two best places are the Pokemon League and Cerulean Cave. Cerulean Cave is probably slightly more efficient, as you don't have to waste as much time with text boxes and flying back to the Indigo Plateau. In either case, speedup and turbo can be very helpful.

If you have an EV friend you've been preparing throughout the game, you shouldn't have to grind for too long. If not, you can buy 10 of each vitamin to get a head start and then start grinding.

(Thanks to many users in the comments for their suggestions, including but not limited to lordpsycho, Shwoo, Renan007, Mophmeister, darkXhadow, Bushando64, ATLow, BladeofLeaves, Merricide, DestroyingSanity, and CinnamonKilljoy)

Catch 'em All Achievements

Uno, Dos, Tres! (25)
Catch the three legendary birds.

MISSABLE

This achievement is missable if you KO any of the legendary birds without catching them, as they won't respawn. Make sure you save before fighting them, just in case!

Articuno is located on the lowest level of the Seafoam Islands, Zapdos is located in the Power Plant off of Route 10 east of Cerulean City, and Moltres is located in Victory Road. As stated earlier in the guide, the easiest way to catch legendary Pokemon in this game is to inflict them with a status and chuck Ultra Balls. Sleep is ideal, but even Paralysis gives a ~10% catch chance at full HP. Alternatively, you can use the Master Ball on one of them, as we won't be using it to capture Mewtwo.

Make sure you save before you battle them - if you KO them, they won't come back!

cOmPlEtElY dIfFeReNt GaMeS (5)
Catch all of your version's exclusive Pokemon.

Here are the version exclusives for each game:

Red	Blue
Ekans	Sandshrew
Arbok	Sandslash
Oddish	Vulpix
Gloom	Ninetales
Vileplume	Meowth
Mankey	Persian
Primeape	Bellsprout
Growlithe	Weepinbell
Arcanine	Victreebell
Scyther	Magmar
Electabuzz	Pinsir

Gotta Catch 'em All (50)
Catch all 124 Pokemon possible in either game without outside trading.

MISSABLE

This achievement is missable if you KO any of the legendary Pokemon or both Snorlaxes, if you use or lose all of your Moon Stones without getting all the evolutions (except Wigglytuff, who appears in Cerulean Cave), or if you do something silly like releasing Eevee, your starter, or Omanyte/Kabuto before evolving them.

You'll need to catch all the Pokemon possible on a single cartridge (without glitches). To be very specific, you'll need to catch all the Pokemon EXCEPT:

The two starters you didn't pick, and their evolutions
- e.g. if you picked Bulbasaur, you wouldn't need to get Squirtle, Wartortle, Blastoise, Charmander, Charmeleon, or Charizard.
The Mt. Moon Fossil Pokemon you didn't pick, and its evolution
- e.g. if you picked the Helix fossil, you wouldn't need to get Kabuto or Kabutops.
Two evolutions of Eevee (as you can get only one)
- e.g. if you evolve Eevee into Jolteon, you wouldn't need to get Flareon or Vaporeon.
The Pokemon from the Fighting Dojo that you didn't pick
- e.g. if you picked Hitmonlee, you wouldn't need to get Hitmonchan
Pokemon evolutions obtained through trading
- i.e. Gengar, Alakazam, Machamp, and Golem
The version exclusives of the game you're not playing
- e.g. if you are playing Blue Version, you wouldn't need to get Ekans, Arbok, Oddish, Gloom, Vileplume, Mankey, Primeape, Growlithe, Arcanine, Scyther, or Electabuzz
Mew

If you're counting, that's 27 Pokemon you don't have to get, giving us our final total of 124. Some people have reported difficulty in getting this to pop, so I took a look at the achievement logic to see the specific requirements. I'm not a developer, but from what I understand, if you catch any Pokemon you're not "supposed" to have, it will prevent you from getting the achievement no matter how they were acquired. For instance, if you have two different starters, two Eeveelutions, or any of the version exclusives from the opposite version, the achievement will permanently be unobtainable unless you start a new save file. This is true even if you encounter them via a glitch instead of trading for them - all the achievement cares about is the "caught" status in the Pokedex.

Mew may or may not be an exception. Some players have reported that they were able to get the achievement while capturing Mew, and the achievement logic doesn't seem to prohibit it as far as I can tell. Still, catch it at your own risk.

You'll likely need to grind up levels on several Pokemon to fully evolve them. The best way to do that is probably to run through the Elite 4 with one Pokemon that can sweep (preferably your EV Friend to reduce further grinding), and the Exp. All. Try to only bring Pokemon you need XP for, as that will maximize the amount of XP per Pokemon. Alternatively, you could train on wild Pokemon in Cerulean Cave. You'll get less XP per Pokemon, but you won't have to deal with all of the text boxes and flying back to Indigo Plateau that comes with the Elite 4.

Here is a list of all the Pokemon that you strictly must evolve by leveling instead of catching their evolved form, the level you have to get them to, and the best location(s) for catching the pre-evolution to minimize grinding.

Pokemon	Level required	Best Location
Starter	32/36	Pallet Town (level 5)
Butterfree	10	Route 25 (Level 8/9)
Beedrill	10	Route 25 (Level 8/9)
Pidgeot	36	Route 21 (Level 30/32)
Persian (Blue)	28	Route 8 (Level 20)
Primeape (Red)	28	Route 8 (Level 20)
Tentacruel	30	Route 19/20/21 (Level (30-40)
Rapidash	40	Pokemon Mansion (Level 36)
Gyarados	20	Route 12/13/17/18, Fuchsia City (Level 15) (use Super Rod)
Omastar/Kabutops	40	Cinnabar Lab (Level 30)
Dragonite	55	Celadon Prize Corner (Level 18 (Red)/Level 24 (Blue)), Safari Zone (Level 15)

All other Pokemon either evolve through stones, don't evolve, or are able to be caught in their fully-evolved form, often in late-game areas like Seafoam Islands, Power Plant, Pokemon Mansion, Victory Road, or Cerulean Cave. I'll leave it up to you to decide if you want to catch them fully evolved or grind up the pre-evolutions.

Game Corner Achievements

To get all of the Game Corner achievements, you'll need 32,170 coins in Blue, and 36679 coins in Red. If you bought all those coins outright, it would cost you 644,000 Pokedollars in Blue, and 734,000 Pokedollars in Red. Thankfully, by playing the slots (and with some savvy saving), we can cut that cost down considerably.

First of all, you're going to want to pick up all the free coins on the floor and from the patrons:

Pleading Face (5)
Find all the free coins in the Celadon City Game Corner.

From Bulbapedia:

After you pick up the free coins, save and start playing the slots. This video explains the full mechanics, but the gist of it is that the best strategy is to head to the bottom right machine and use speedup and turbo-A to play the machine as quickly as possible. If you're unlucky, you'll run out of coins, but otherwise you should see your stash slowly start to creep up.

Second Place Isn't Bad (5)
Win a Bar at the Celadon City Game Corner.

7 Grand (5)
Win a Jackpot at the Celadon City Game Corner.

Gambling Addict (10)
Win 3000 Credits from Slots without leaving the Game Corner.

So, rich... (5)
Have 9999 Coins at once.

You'll likely get a Bar and a Jackpot on your way to earning 3000 coins. If not, just keep playing. Once you get 3000, you can either continue to play, or if you have the funds, you can switch to buying coins outright. Once you hit 9999, save and get ready to start buying TMs.

Disk Collector II (10)
Buy 1 of every TM you can buy from the Department Store and the Game Corner in one emulator session without resetting.

To do this, you'll need 16500 coins, and 20000 Pokedollars. If you're buying the coins outright, you'll need 330,000 additional Pokedollars.

If you're following from above, you should have enough coins to buy TM15 Hyper Beam and TM23 Dragon Rage, leaving you with 1100 coins. Gamble or buy your way back up to 7700, and buy TM50 Substitute. Then, buy all the TMs at the Celadon Department Store. Once the achievement pops, go ahead and reset your game to the earlier save, when you had 9999 coins, and get ready to buy the Pokemon.

This Is Illegal, You Know (10)
Buy all of the Game Corner Pokemon in one emulator session without resetting.

If you're playing Pokemon Blue:

You should initially have enough to buy Porygon and Pinsir from the middle window, leaving you with 999 coins.
Gamble or buy back up to 6670 and buy Abra, Clefairy, and Nidorino from the left window and Dratini from the right window. Congratulations! You're done with the Game Corner!

If you're playing Pokemon Red:

You should have enough to initially buy Dratini and Scyther from the middle window, leaving you with 1700 coins.
Gamble or buy up to around 3000 coins, then buy Abra, Clefairy, and Nidorina from the left window, leaving you with about 1000 coins
Finally, gamble or buy all the way back up to 9999 coins, at which point you can buy Porygon. Congratulations! You're done with the Game Corner!

Note that you do need Porygon for the Pokedex, so don't reset afterwards to get your money back.

Safari Zone Achievements

Getting Your Money's Worth (5)
Catch 10 Pokemon in a single Safari Hunt. (No resetting)

Before you head in, it's probably a good idea to switch to a new Pokemon Box so you don't run out of space halfway through.

As several users note, pretty much the only feasible way to do this is to catch Magikarp. Each ball thrown has about a 30% chance to catch Magikarp, so it's unfortunately just a matter of RNG. Thankfully, getting 10 Magikarp isn't too unlikely - there's about a 35-40% chance you'll be able to do it within 30 balls. Don't bother throwing rocks - as 14ausher notes, rocks don't boost Magikarp's catch rate because it's already maxed out.

Have Fun (25)
Catch Chansey, Scyther or Pinsir, Tauros and Kanghaskan in the Safari Zone in one emulator session. (Multiple Safari Hunts are fine)

First of all, let's clarify what it means by one emulator session. You can do a soft reset by pressing A+B+START+SELECT, but don't press the reset button on the emulator. You can use as many Safari Hunts as you want, or you can soft-reset after each one to save Pokedollars if you'd like.

Four Pokemon doesn't seem that bad, but these are four of the rarest and hardest to catch Pokemon in the Safari Zone. Thankfully, there are a few things we can do to even the odds a little bit.

The first thing is the Repel Trick. When you use a Repel, you will only encounter wild Pokemon who are of a higher or equal level to the Pokemon in the first slot of your party. So, if you strategically place a Pokemon with a specific level in the front of your party, you can eliminate lower level encounters and give yourself a greater chance of finding the Pokemon you want. If you need a Pokemon with a specific level, you can probably find one in the Safari Zone itself. This trick does require a bit more effort, so you might find it easier to just run away from the extra encounters, especially if you're using speedup.
The second thing is to strategically choose which area you're looking in. Each Pokemon has one area with a 4% encounter rate and one area with a 1% encounter rate. Obviously, we're going to want to go to the area with the 4& encounter rate for the Pokemon we're trying to catch.
The third thing is to use the soft reset by pressing A+B+START+SELECT. If you save right when you get to the patch of grass you're hunting in, you can soft reset when your steps run out and get right back into the action instead of walking from the entrance again. This will save a ton of time, effort, and Pokedollars in the long run.
The final thing is not to bother with rocks or bait. To make a long story short, the best strategy in the Safari Zone is just to keep throwing balls. If you run low on Safari Balls it might actually be better to throw a rock or two for certain Pokemon, but because we'll likely be using a lot of steps to generate each encounter, it's unlikely that you'll get low enough for it to matter. You can use the calculator at the bottom of that page to see the odds for yourself, if you'd like.

With these four tips in mind, here's tips for each individual Pokemon:

TAUROS

Found in Area 3 (west) at level 26
6.62% chance of catching per ball, 12.09% chance of catching before it runs away

CHANSEY

Found in Area 2 (north) at level 26
4.07% chance of catching per ball, 13.78% chance to catch before it runs away

SCYTHER/PINSIR

Found in Central Area (entrance) at level 23
Pinsir in Blue, Scyther in Red
Pinsir: 6.62% chance of catching per ball, 16.18% chance of catching before it runs away
Scyther: 6.45% chance of catching per ball, 13.62% chance of catching before it runs away

KANGASKHAN

Found in Area 1 (east, aka Central Area East) at level 25
6.62% chance of catching per ball, 14.62% chance of catching before it runs away

If you use speedup liberally and the soft reset trick mentioned above, it should make this grind a lot more manageable. If you need to pause, you can minimize the emulator, but don't close it or close the game or else you'll have to start all over again.

Have fun!

(Thanks to many users in the comments for sharing strategies, including but not limited to lordpsycho, mquay2, Lestatfrost, TindalosKeeper, Cavi3D, MarvellousDazza, Greatscoot, Eliaaa, and Loran)

Battle Achievements

Gone Critical! (5)
Land a Critical Hit 5 turns in a row in a single battle.

As stated in the Intro, critical hits in this game depend on a Pokemon's Speed. Here's the nitty-gritty, but the short of it is that a Pokemon using a move with a heightened critical chance (i.e. Slash, Razor Leaf, Karate Chop, or Crabhammer) that has 64 Speed or higher will always crit. Well, almost always (thanks, Gen 1). 64 Speed really isn't all that much, so you have a pretty decent chance of accidentally getting this if you use Slash a bunch of times back-to-back.

Hilariously, using the move Focus Energy or the Dire Hit item will actually lower your chance to crit, due to a bug.

Target Acquired (5)
Land 5 One-Hit KO moves in a row in a single battle.

To get this, you'll have to land one of the OHKO moves (Fissure, Guillotine, or Horn Drill)

As Trufa (and others) mention in the comments, the secret is to use the X Accuracy item, which will bypass accuracy checks for every move, making them always hit. Add in an X Speed or two, and you should be able to take down a member of the Elite 4 easily. If you don't have a Pokemon with an OHKO move, you can catch Rhydon in Cerulean Cave, as Mekevin255 suggests, or buy TM07 (Horn Drill) from the Department store and teach it to a compatible Pokemon.

Stalemate (2)
Survive 20 turns in a battle without switching out or having either Pokemon be harmed. (Must be at Max HP, status is fine)

The easiest way to do this is (as the icon suggests) to go to Viridian Forest and catch a Metapod/Kakuna that knows Harden, put it in the front of your party (make sure it's at full HP), and fight another Metapod/Kakuna that only knows Harden. You could do it with a Splash Magikarp as well.

Surprise Mechanics (3)
Use Metronome to go out with a bang.

Clefairy (but not Clefable!) learns Metronome at level 31. Otherwise you'll have to use TM31 to teach it to a compatible Pokemon.

To get this achievement, you'll have to use Metronome (a move that selects a random move) until it hits Selfdestruct or Explosion. Unfortunately, this is just up to random chance. You'll probably want to find a patch of grass relatively close to a Pokemon Center, and just keep trying until you get it.

I Found You, Faker! (2)
As Ditto, use Transform on an Enemy Ditto.

You'll have to catch a Ditto, and then use Transform on an enemy Ditto. Ditto can be found on Routes 13, 14, and 15 east of Fuchsia City, Route 23 leading to the Pokemon League, and in Cerulean Cave.

I Was Frozen Today (5)
Be cured of being Frozen in battle without using an item in that battle.

In Generation 1, the Freeze status lasts until cured by an item, or until the Frozen Pokemon is hit with a Fire-type move. For this achievement, you'll have to get a frozen Pokemon. There are a few ways to do this:

As Earthsouls and WKGames suggest, you can get frozen by an enemy's attack. Wild Articuno has Ice Beam, and Lorelei's Jynx and Lapras have Ice Punch and Blizzard, respectively. Each of these attacks have a 10% chance to freeze. Note that Aurora Beam, used by some of Lorelei's other Pokemon, cannot freeze the target. To get Lorelei to use Ice Beam, send in a sturdy Pokemon weak to Ice, as poisongirlss suggests.
As Vermilion suggests, you can freeze a wild Pokemon and then catch it.

Once you have your frozen Pokemon, you'll have to find a wild fire-type Pokemon. As the commenters note, the easiest place is in the Cinnabar Island Mansion, where you can find wild Ponyta who know Ember. Wait for them to hit you with Ember (wild Pokemon choose moves randomly), and the achievement should be yours!

Wario Would Be Proud (5)
Generate over $2000 in a single fight using Pay Day.

MISSABLE (in Red)

Whenever Pay Day is used, it scatters coins equivalent to twice the user's level. Therefore, in order to get more than 2000 Pokedollars in a single battle, you'll have to have a Level 50+ Pokemon use all 20 PP. If you want, you can decrease the level requirement by using Ethers or PP Ups to increase PP.

In both versions, the easiest way to get this achievement is probably to use the Pay Day TM (TM16) to teach the move to a level 50+ Pokemon (many Pokemon found in Cerulean Cave can learn it) and go into an Elite 4 battle to use all 20 PP. As WKGames suggests, Lorelei's Dewgong may be a good choice, as it can use Rest to recover.

If you already tossed or overwrote the TM, you'll have to train up a Meowth if you're playing Blue, possibly using Ethers as described above if you don't want to go all the way to 50.

The last option is to fight a Trainer with Meowth or Persian. Even if your opponent uses Pay Day, you'll still get the money at the end of the battle. What's more, enemies in this game don't actually have PP, so they can keep using Pay Day infinitely. So, if you pack a bunch of healing items and let them hit you with Pay Day over and over again, you should eventually get this achievement.

Eight trainers have a Meowth:

A Female Jr. Trainer on Route 9 East of Cerulean City
Two Female Jr. Trainers in Rock Tunnel
A Lass on Route 8 east of Saffron City (she has 3 Meowths)
Another Lass on Route 8, right next to the previous one
A Female Jr. Trainer on the west side of Route 13
A Beauty on the west side of Route 13
A Female Jr. Trainer on the east side of Route 13

Two Trainers have a Persian:

A Female Cooltrainer on the first floor of Victory Road
A Tamer on the second floor of Victory Road.

Each of these Meowths/Persians should have Pay Day. If you're playing Red and you're desperate, try facing one of them!

Acknowledgements

Thanks to the talented staff at Game Freak for creating a classic game, and debatably an entire genre.
Thanks to Blazekickn and dude1286 for creating an excellent set that holds a dear place in my heart.
Thanks to Bulbapedia, StrategyWiki, Smogon, zerokid, and Fabio Attard for their excellent resources. I have used images from Bulbapedia and StrategyWiki in several achievements, as well as portions of Fabio Attard's checklist for the relevant achievements.
Thanks to the many RetroAchievements commenters who have shared tips and strategies in the comments. I've tried to cite users as appropriate, but with such a popular game it's inevitable that I've missed some.

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Misc. Pages
WIP Guides

Pokemon Red and Blue Versions (Game Boy)

1) Synopsis / Table of Contents

2) Introduction

3) General Information

Pokemon Basics

Generation 1 Differences

Red or Blue?

Glitches

Achievement Set Tips

Useful Resources

4) Walkthrough

Step 1: Story | Total points: 336

Boulder Badge

Cascade Badge

Thunder Badge

Rainbow Badge

Marsh Badge

Soul Badge

Volcano Badge

Earth Badge

Victory Road

Step 2: Elite 4/Postgame| Total points: 95

Elite 4

Cerulean Cave

Step 3: Catch 'em All/Miscellaneous | Total points: 354

Adventure Achievements

Catch 'em All Achievements

Game Corner Achievements

Safari Zone Achievements

Battle Achievements

Acknowledgements

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