This achievement is obtained after dealing damage 300 times with Firearms. This can be done with either pistols or rifles, but pistols can be shot faster. You can grind this out easily on Guardians as they have a ton of health and can soak up just about as much ammo as you can spare.
You can find ammo for your firearms by searching the containers in cities, looting dead enemies, purchasing from merchants and crafting it yourself if you have Alchemy leveled up to 2.