Weapons that count:
The first shotgun you will get will probably be the W1300 during the 3rd chapter, although there are plenty littered throughout the game. They are not very powerful unless you are very close range, so keep this in mind. Just rotate through whatever weapons are available to you, and you will get this achievement with natural progression.
If you are desperate for kills, start Chapter 6, go to the right hand side to pick up the shotgun and kill as many enemies as possible. Then reload the checkpoint.