i beat the game with having a least 1 bullet left at the end of each level
All but one level can be cleared without using the gun at all.
Someone claimed it was every level, but I don't see how you can do the four armored guys on glass without the gun. I might go back and see if I can do it with only one bullet.
Edit: Might be possible with one bullet. Extremely hard.
Looks possible with two bullets. Very hard.