This achievement is simply for killing enemies with your axe or guitar.
You'll get the achievement naturally over the course of the game as you do side missions and the main quest-line.
Upgrading your weapons would help you to kill them easier.
Obviously this achievement is easier to get on earlier enemies that aren't as dangerous as the later ones.
I unlocked this one before getting to the ice area of the map by just doing the main quest and a few side missions.