For this achievement you must kill at least 75 enemies throughout the course of the game using guns. The final killing blow MUST be from a gun.
The easiest way by far to achieve this is to unlock the Unlimited Submachine Gun and use that the entire game. Just be warned that the gun may freeze your game due to the attrocious framerate this port has, it did for me once.
Also note that playing on a higher action difficulty setting offers more monsters to kill. This achievement popped for me at the end of the Sewers, and I was playing on Normal.