This achievement simply entails that you kill someone. It doesn't matter if it is a guard, a civilian or a target. Just kill them in anyway. If you want this out of the way immediately, then simply kill a fellow inmate or a SWAT member on the first level with any method.
If you want to unlock this with 2 other achievements, take a pistol from the start and get a head-shot on one of your fellow patients. This will unlock you an achievement for getting a kill, killing an innocent AND getting a head-shot. 3 achievements in less than 3 seconds.