Distrust

This achievement will most likely take you several games to actually get. Bullets are in very limited supply and you typically get five or fewer per game. I've, very rarely, gotten more than six, but never more than ten. It's all up to the randomness of the game.

In order to actually use the gun, you need a target and a bullet. You can't just randomly fire. Your main options are to shoot locked doors. Otherwise, you can shoot the anomalies that spawn when you sleep. However, the eye, ice, and lightning anomalies can all be dealt with by other means. Shooting is the only way to deal with the humanoid anomalies found in zones 4 & 5.

An alternative method is to wait on this, or at least not strenuously work towards it, till you unlock Nicole Steelman (done by achieving the Second Bad Ending). She starts the game with a gun and 4 bullets. Simply go around the buildings and shoot the doors. Save & Quit. Start a new game. Rinse and repeat till done.

Bleep blood. Achievement unlocked. Hope this helps.