Experimental Fiction - Complete all levels in Typing of the Dead (plus 8 others).
May as well start here. Just play through all 9 stages of Typing of the Dead, you can even pick the easiest difficulty if you like. You will receive one achievement for each stage. You don't even need to do anything special and you have infinite continues. Throughout this play-through you will likely get achievements for headshots and fat zombie mutant kills and add towards progression on rage zombie mutant kills (though there is no progression displayed for this).

Sideshow Wizard - Play all mini games in Typing of the Dead.
Another very easy achievement, just go to the Mini Games menu and try each one. You don't need to beat any scores, just play them once and you're done.

Fingers of Fury - Complete all Hardcore levels in Typing of the Dead (plus 1 other).
Now you've beaten the game once, you have unlocked Hardcore mode. Don't be afraid, its not so bad. Only difference with Hardcore is that if you make a typing mistake, you have to start the phrase over again - and you're given a new phrase to type. You can still pick easy difficulty, and you have infinite continues. There is unfortunately no tracking. This play-through will also add towards your rage zombie mutant kills.

Knee Trembler - Maintain a Goregasm for two minutes in Typing of the Dead (plus 1 other).
To achieve a Goregasm, you will need to kill roughly 20 zombies mutants without getting hit or making a typing mistake. To maintain it, you cannot get hit or make a typing mistake for two minutes. If you're going for all achievements anyway, you will likely get this when going for the No Damage achievements. There is a trick though - at a number of points in the game, you will reach a zombie mutant that constantly throws objects at you. If you have a Goregasm before reaching one of these zombies mutants then leave him alive and constantly shoot the projectiles. The achievement will pop after 2 minutes and you can continue on your way.

Easy Targets - Kill 100 Fat mutants in Typing of the Dead.
You won't be able to miss this one. You'll probably pick it up sometime around the 4th stage.

Boom, Headshot! - Decapitate 200 mutants in Typing of the Dead.
This one will come over time as you get better with the game. To score a headshot, you need to type the phrase without error. Your majority of kills in Hardcore are going to be headshots, so don't worry about this one.

Temper Temper - Kill 30 rage mutants in Typing of the Dead.
These zombies mutants are the ones you need to hit 3 parts of their body before finishing them off with a hammer/pipe/etc. Like the other kill-based achievements, there is no progression for this. There also isn't 30 rage zombies mutants in an entire play-through either. After beating both the standard game and then hardcore, I still had 14 more rage zombies mutants to kill before the achievement popped. Thankfully, you do not need to play through an entire stage. Fire up Scream Train, shoot the first 7 or so regular zombies mutants and a rage zombie mutant will show up. Hit him 3 times then view the little cutscene where he's finished off with the knife. Once the camera starts moving again, quit the stage and repeat. It says your progress will not be saved, but it still saves the achievement progression.

Nifty Fingers - Type a thirty character phrase without any errors.
In order to get a thirty character phrase to appear, you will need to play on Hard difficulty. For a better chance at a phrase appearing, play on Hardcore. If you reach a zombie mutant thats a fair distance from you, you can intentionally make an error and you'll be given a new phrase. There is a chance you'll get this while doing the No Damage achievement, but I wouldn't risk it in the same play.

Untouchable | Mad Motor Fingers | Digits of Destruction - Complete a level without taking any damage in Typing of the Dead (plus Hardcore and Hard difficulty).
These are the real challenge in Typing of the Dead. A true test of your typing skill and patience. I admit, I was ready to accept defeat on these achievements until I read Hybrid Killer's guide. Using the same technique for Hard difficulty also helps to improve your chances too.

In addition to Hybrid Killer's tips, I will add a few more, specifically for Hard difficulty:

• Do not stress about civilians, you do not lose health if they die.
  
• If your phrase is too long, then intentionally make a mistake early to get a new word, chances are it will be shorter.
  
• Do not go out of your way for collectibles, they can be distracting.
  
• Save the slowdown power-up for when you have plenty of enemies on the screen already.

If you're feeling lucky, you can get all 3 achievements in a single play. As Hybrid Killer states, Hardcore mode is the key to getting these.

Killing Over - Complete all levels in House of the Dead (plus 8 others).
May as well start here, just progress through the levels as you see fit. Your starting weapon is extremely weak, as soon as you can buy and upgrade a better weapon. I preferred the Automatic Shotgun. Assault Rifle is 3-round burst which can be good for boss fights, but having a zombie mutant jump up right in between your burst can hurt. Any collectible progression you make here will count towards the challenges in Director's Cut. As you progress, keep an eye out for a 5-kill opportunity for the Toasty! achievement. Upgrade your guns of choice, but don't upgrade all guns just for the sake of it, there's a surprise waiting......

Toasty! - Kill five or more mutants with one grenade.
Shoot grenades during the stage to collect, use them with right-click. Keep an eye out for opportunities for this as you play through the game. A couple of easy spots are on Naked Terror, just outside the club there are a group of them eating carcasses on the road. Alternatively, there are a few large groups in Creeping Flesh.

Lights, Camera, Slaughter! - Complete all Director's Cut levels in House of the Dead.
Director's Cut is a separate section from the main menu, unlocked after beating the regular Story Mode. Level progress is tracked, unlike Hardcore mode in Typing of the Dead. Your gun upgrades carry over from Story Mode, also you'll have the minigun unlocked for purchase at a sweet $15,000. You can use this play-through to work on some of the challenges if you like, you will need to replay this mode a lot if you want that achievement.

Challenge Accepted - Complete all challenges in all Director's Cut levels in House of the Dead.
This is the last achievement I have left to the game, and I must admit it has got the better of me. This one is for the truly dedicated. I don't know about you, but I got the game for its typing mode, this achievement just seemed an excessive excuse to play the original mode. Most of your time will be spent here, not the Typing mode. In any case, this wouldn't be much of a guide if I neglected to give the run-down on this one.

Any challenges you completed on your previous Story Mode run will carry over, most noticeably any collectibles you've already collected.

Each stage has 7 identical challenges (though their target values differ) and can be completed at any time. Going for all at once is possible (almost required to get a high score), but extremely unlikely due to the random nature of the camera. Thankfully they can be completed over multiple play-throughs.

• Combo - Don't miss a shot, don't get hurt. This goes hand-in-hand with Accuracy. Once you reach the goal combo, you can forget all about accuracy, but then you'll miss out on that challenge too. This one wasn't so bad, I used the Auto Shotgun.
  
• Accuracy - Don't miss a shot for the entire level. You can take damage and your accuracy won't drop, but you'll lose life. You could make use of your infinite continues and be patient with every shot to make this easier.
  
• Goregasm - I'm honestly not sure what the difference is to Combo. Kill things, don't get hit.
  
• Player Deaths - On a scale of 1, so... don't die. You can take damage, just don't lose all your life. Straight forward enough, right?
  
• High Score - Each stage has its own target score that you won't find out until you complete the stage. In all cases, the only way you'll reach the high score is if you don't lose your combo, rescue all civilians and pickup all collectibles. Basically, do all challenges simultaneously.
  
• Pickups Collected - This can be picked up in multiple play-throughs. Pickups are only the audio tracks, posters, 3d models, not health or slow-down powerups. Director's Cut levels have a few collectibles in places that can't normally be reached in Story mode. There are a number of collectibles that only appear on the screen for a fraction of a second before the camera moves on, so try and remember them for subsequent plays.
  
• Civilians Saved - Save them all. Annoyingly, you can kill civilians who love to stand in the line of fire, or will move into your crosshair as the camera moves around. Civilians will die from a single bullet of the weakest weapon on any part of their body, which can lead to yet more frustration. Their 5000 bonus points each are essential to reaching a high-score.