To unlock this achievement, the player must clear each of Evan Wright's levels (including The Abyss) without killing any enemies. The mobster outside the building in First Trial must be killed and does not count against this achievement.
Avoiding killing any enemies during executions is quite easy; Evan will not respond to a click that can be deemed "lethal" - rather, he will play a short animation where he uncomfortably moves his arm/weapon back. Clicking after the animation finishes, however, will make Evan use lethal force on an enemy.
Do not worry about enemies knocked into walls; they can't be killed.