To unlock this achievement, you will need to perform Co-Op combos, until you have a x10 combo. This achievement is quite difficult, but the best places to obtain this are when you get to choose whether you operate a turret, either on the back of a truck while your partner drives, or in the helicopter, where your partner stays on the ground.
This is easiest unlocked during the mission 'Assault', when you are in the quarry. You should choose to operate the mounted mini-gun on the helicopter and shoot at every enemy you see, possibly using Overkill if you have it ready. The achievement should unlock after killing around 10 enemies here. If you do not unlock it, you can reload the checkpoint to try again.
I got this achievement cos I was on the back of the truck shooting enemies down while the NPC partner inside the truck mows them down before it hit the wooden gates. It's the only way to do it without ending the combo kills.