From Scratchpad

This is a tutorial for gun skills. Talk to the Third Home weapons shop NPC and he will hand you a Featherlight shotgun and thirty bullets. Talk to him again and he will explain how to use guns in this game.

He will then ask that you kill five Cait Siths. Do so, and your reward will be the Featherlight shotgun you just got and one Sweeper handgun.

You do not need to use the shotgun to kill the Cait Siths.