A kill in this game counts as you personally killing someone, or by your actions with machinery (like rewiring an arc wall and a guard walking through). If you knock out someone, and they are eaten by rats, that does not count as a kill. Instead of engaging enemies, try to sneak around them. If that fails or you can’t see a way around, then you always have your sleep darts to rely on. The game will give you a choice for a couple of characters, make sure to choose things like capture or spare instead of kill. You will know at the end of each mission if you never killed someone as a box will be checked that says "Didn't kill anyone". If you need help with this trophy, please see my pure stealth walkthrough for a text walkthrough as well as videos.