Perform a melee kill while you're in Overkill

To get into Overkill, you will need to kill enemies until your Overkill meter on the right hand side fills up. Then you need to press LB and you will go into Overkill, where you will become invincible for a short time. While you're in this mode, you need to run up to an enemy and press RS and you will melee kill them, violently, unlocking the achievement.