Easily done in the first few "tutorial" missions. For me, in mission 2 I killed 7 spiders bare handed, going back to the healing spring in between fights. When 3 spawn, lead them onto a narrow bridge to fight one at a time. This got me the achievement for completing a level without weapons. Got my next three on the third mission, weakening the enemies with spells than punching to finish them off. The achievement pops the moment you kill 10, so you can redo the level if you took too many hits trying for the three punch kills.
Edit: You can begin working toward this on the first mission, just make sure to unequip the cudgel before exploring the labyrinth for the first time.