This achievement is fairly simple to get.
You can either beat them to death, in which case, you should upgrade the melee damage to max. Or, you can use the axe to kill them. The axe DOES count towards melee kills.
I would also like to clear a few things up in relation to this achievement.
I got this on my New Game + play-through while I was getting all the collectibles. Melee kills from your previous play-through will carry over to NG+.
Stealth kills DO NOT count towards this achievement.
You DO NOT need the knuckle-duster to get this.