This is a bit of a trick trophy and is the reason you will need to play half of the game again (sort of) and it is important to know that you need to start a completely new game. You can't use chapter select and you can not carry over progress from your past play. This trophy works by reading the stats of your save file and if you carry progress over from the previous game, your kill total will not be at 0. When you start a new game, make sure it is a fresh new game and that your game stats are all blank at the start of the game. This way you can be 100% sure you are starting with a clean slate.
To get this trophy, you need to make it to the start of chapter 5 using only your fists. No guns, grenades or any weapons. Doing this on crushing is definitely going to be impossible. This is best done on Explorer difficulty, this way you can run past groups of enemies, take a bunch of damage and not get killed by it. You need to run past enemies when you can and if you are stuck in a scene with combat you will need to use your fists to take out all the enemies. It doesn't matter if Nadine kills enemies, it only counts for you. If you shoot a gun, even by accident and it doesn't hit anyone the trophy will become void and you will not be able to unlock it.
The best strategy for this is to use a lot of manual saves. After playing through the game once, it will be a reflex at times to shoot. If you do it by accident, you don't want to have to start the entire thing again, so make a manual save (not an auto save) and reload this when you screw up. Stealth is your best friend, make it through areas without engaging with enemies whenever possible. Use silent take downs to get rid of enemies rather than jumping out in the open. It doesn't matter if enemies do spot you, but it is a lot easier for you if you can slip through without them noticing.
The trophy will unlock at the very start of chapter 5, so if you are into this chapter and it has not unlocked, then you must have shot a gun or something.
Some people have reported that dying invalidates this trophy. To play things safe, make regular game saves and if you die, reload the save. The trophy should allow deaths, but the glitch may prevent you from being able to unlock it.