This is fairly easy if you be careful with people you knock out/put to sleep. If you leave someone laying on the ground then rats may eat them or weepers may attack them getting you a kill. Make sure to move them to an area that there are no paths for anything to get to. Unconscious characters that fall from a height or into the water will die and it will count against you.
You need to get all the the targets and dispose of them non-lethally. I have a guide here:
Killing anything non-human such as rats, dogs, fish, river krusts or anything else won't affect the achievement. The end mission screen tells you if you killed anyone.