Only two weapons count towards this:
• Taiga's Crossbow
• Dead City's Hellsing
The good thing is you can retrieve your bolts from dead enemies so, you don't need to feel like this is a grind.
If you want to stop Alyosha from being injured. Pick on wildlife during Taiga and there are plenty of Mutants in Dead City to make up the numbers.
Best place to do this is in Dead City at the end of the Battleground. When only one enemy is left, reload the checkpoint and do it again. The tropht is cumalative during one playthrough.