There are four shotguns in the game, the duplet, the shambler, the bigun, and the Azbat. Any combination of kills can earn this achievement. I recommend always carrying a shotgun. They are the most effective weapons against mutants
You'll receive the duplet near the end of the second level, on the cart ride.
The shambler can be purchased in Riga, or found on enemies afterwards. You should have one for your first trip to the surface. It is very effective at chewing through 2-3 mutants, but has an awkward reload. With an extended barrel, it has the best range of any shotgun, making useful vs. Humans, too.
The bigun can be purchased in polis or the ranger station. It's good for killing demons and librarians, but little else. The shambler is more effective in general.
The azbat is found in only in the ranger station. It's like the bigun, but with more rounds and accuracy.
Your best bet for this trophy is using the shambler anytime you face hordes of mutants. The trophy should come quickly that way. If you need to grind it, reload armory, purchase a shambler with the extended barrel mod, and proceed to frontline. Kill everyone with the shambler.