The one bullet must be fired during the level "Lowlife". The room where you get the shotgun and the 9mm is entered through the A/C vents and can only be exited by SHOOTING the lock on the door. If you miss the lock, then you should stop playing video games.
After you fire your one shot, proceed through the game whilst only using grenades, rockets, crowbars, and the Gravity gun.
Grenades are limited so use against large groups of enemies and snipers located in the windows.
Rockets are mainly useful against gunships but can also be used during the civilian evacuation near the end as there are plenty available in both scenarios.
Apart from using the crowbar in confined spaces, your best bet is the Gravity Gun since it essentially has unlimited ammo and kills most enemies in one hit from anything.
If you do feel the need to cheat (even though this achievement is already very easy without them), use the above Invincibility cheat to get in close with the crowbar and use the Ammo Spawn cheat (Y, B, A, X, RB, Y, X, A, B, RB) to restore your rockets and grenades.