Simply put, kill 5 Psychopaths in Co-Op
You can also do this in Sandbox Mode from what I hear.
Being fast is key here as this achievement can be glitched in various ways.
1. If your Co-Op partner ends up leaving or getting disconnected during a Psychopath fight, they will not get credit toward the achievement.
2. If you don't do it in the same run (not shutting the game off) you will go back to 0 killed, only the host will get the achievement.
My partner and I killed Randy and he got the achievement but not me since I got disconnected. I didn't get the achievement until later when I killed the snipers.