It is virtually impossible to get this achievement on the first playthrough since the crossbow used (to dispatch the guards per Jaron Namir's orders) at the beginning of the game is equipped with lethal ammo. The player additionally does not have any other weapon, cannot purchase anything and cannot use takedowns at this point in the game. Therefore on the second playthrough, acquire the non-lethal Tranquilizer Dart modification, attach it to the crossbow and use to get the achievement. But it is important not to hit heads of enemies with it. This would result in a kill and therefore make it impossible to get the achievement without starting a new game.
This has since been fixed via a patch. The crossbow used at this point is now equipped with Tranquilizer Darts by default.