In order to unlock new skill moves, you need to level up (so you will probably get this while just playing the game). I'm not going to put a list here because you can just check your status while in game. But I will say this, the last skill move (Disembowel) unlocked for me at Level 47. I believe it is random what level skill moves unlock on but for me, I got the achievement after reaching Level 47.
just by saving all survivors and doing all missions my first play through, i reached well over level 40. playing a second play though reaching level 50 should be pretty easy.