I'm going to assume that you have beaten the game at least once before trying a knife only run. There are some spoilers in this guide.
In order to unlock this achievement, you have to beat the game using only your knife. It can be done using any difficulty with either character. Chris has a better knife, does more damage with it, and has more health, but Jill is able to skip the Plant 42 boss fight completely. If you start with a handgun/rocket launcher, unequip it and deposit it in an item box as soon as possible.
I did this playing as Jill on Very Easy mode.
Notes
Along with the obvious (firearms), you CANNOT use:
- Defense items. Avoid picking them up. If you do pick one up, go into the options menu and make sure your defense item use mode is set to "Manual".
- Kerosene. This means no burning zombie corpses.
- The zombie head stomp. Playing on Very Easy, I never encountered a crawling zombie.
You CAN use:
- The herbicide against the fountain plant in the mansion's greenhouse.
- The water flow control system unit against Neptune.
- The insecticide against the bee nest in the guardhouse residence.
- The bee squish. Stepping on any bees that are on the floor will not void the achievement.
- V-JOLT against Plant 42. If you're playing as Jill, this will let you skip the Plant 42 boss fight. If you're playing as Chris, you still have to fight Plant 42, but it will start at half health. Also, as Chris, in order to use the V-JOLT, you have to let Richard die by not getting him the serum.
- The rocket launcher against the 2nd Tyrant battle on the helipad. I recommend letting Barry (if you're playing as Jill)/Rebecca (if you're playing as Chris) die earlier on so you can skip the helipad battle completely.
Enemies
You only need to kill one non-boss enemy (well, just one with the knife), and that is the collar wearing Cerberus (dog) on the mansion's outside balcony. Dodge when it leaps at you, then slash downwards at it while it recovers. If you take any damage, there are green herbs in a plant trough. You can't take them with you, but you can heal three times using them. Technically, you do kill bees when you use the insecticide on the nest in the guardhouse. All other non-boss enemies, and even a few bosses can be dodged/skipped/avoided.
Bosses
Yawn (1st encounter in the attic) - Simply run to the back of the attic, grab the death mask, and run back out. Yawn is very slow, so you should be able to grab the mask and get out without getting hit.
Crimson Head Prototype 1 - For me, this was the most difficult boss battle. Wait for the Crimson Head to lunge at you. As soon as it does, run behind him and slash. Run away from him and repeat.
Lisa Trevor (1st encounter in the cabin) - Lisa is invulnerable, so your only option is to run. Try to lure her to attack, then run by her while she recovers.
Neptune - Push the water flow control system unit into the water, then flip the lever.
Plant 42 - If you're playing as Jill and you use the V-JOLT, you won't have to fight Plant 42 at all. If you're playing as Chris and you use the V-JOLT, you will still have to fight it, but it will have half health. Use the stairs and the walkway and slash at the tentacles.
Yawn (2nd encounter in the library) - Climb down the ladder and go to the narrow area behind the bookshelf. Wait for Yawn to come close, then run away and go around the bookshelf until you catch up to its tail. Slash at its tail. You should be able to get two slashes in per lap.
Black Tiger - Lure the Black Tiger away from the door covered in webs. Use your knife to clear the webs and go through the door. You may get hit a few times. There is a green herb and two blue herbs on the other side of the webbed door in case you get injured and/or poisoned.
Lisa Trevor (2nd encounter in the winding underground passage) - Same strategy as the 1st encounter, just run. There are two paths. Lisa will appear in the first path you go down. Start going down one path, wait for her to appear, then turn around and take the other path. This way you won't have to try dodge her by running by her.
Lisa Trevor (3rd encounter in Jessica's tomb) - If you are playing as Jill, you have the option to give Barry back his gun. I recommend NOT giving him back his gun. This will allow you to skip the 2nd Tyrant boss fight later on. As Chris or Jill, simply dodge Lisa and push the stones off of the ledge. If you get too far away from her, she will jump over the coffin in the middle right towards you. As soon as she starts jumping, run away from that spot to one of the other stones. You'll have some extra time to push a stone or two before she catches up to you. If she does hit you, there is a chance she will knock you right off the ledge.
Tyrant (1st encounter in the labs) - Run behind Tyrant, and slash at his backside until he turns around. You should be able to get two slashes in before running around him again. He isn't very aggressive, and didn't try to hit me once while I was running by him.
Tyrant (2nd encounter on the helipad) - This is the boss fight that can be skipped if you let Barry/Rebecca die earlier in the game. If you did save them, you'll have to run around until Brad drops the rocket launcher from the helicopter. Tyrant is much more aggressive this time around. He moves much faster and has quite a bit of range with his claws. He will attack Barry/Rebecca, which will take up a lot of time, but will likely kill them in the process. If that does happen, keep your distance from Tyrant until the rocket launcher drops.
Summary
There are only five monsters in the entire game that you need to kill using the knife: the collar wearing Cerberus, Crimson Head Prototype 1, Plant 42 (optional as Jill; required as Chris), Yawn (2nd encounter), and Tyrant (1st encounter). Every other monster can be dodged/skipped/avoided or defeated with the environment
If you have any questions, please let me know.