Very simple kill 300 creatures. Doesn't matter how or what you kill them with as long as they die lol.
Creatures include: Radroaches, Molerats, Bloat Flys, mirelurks, ants, Centaurs, Deathclaws, Yao Guai, Radscorpions, etc.
Note: It seems that Super Mutants also count towards the 300.
Pretty much anything that isn't humanoid.
You can check how many creature kills you have on the Stats screen.