Army of Two (EU)

This solution is based around playing coop.

Step 1: Play through mission 3 Iraq until you get the checkpoint on the bridge while you pursue Ali Youseff.

Step 2: After crossing the bridge Rios and Salem talk about coop sniping the 2 enemies by the barrels.

Step 3: Kill them then one of you should hop on the turret. You cannot get overkill while on the turret so fill up your aggro using it then get off.

Step 4: Start shooting with your primary gun and you should quickly have overkill.

Step 5: Activate overkill and Kill the enemies in the surrounding area and reload your checkpoint( Remember to take it in turns unless only one of you needs the achievement). The checkpoint is just behind the turret so the kills are much quicker than other solutions.

Step 6: Do this until you have the achievements for each player then swap places. This will net you both achievements for both players fairly quickly.

It is much better to do this with a coop partner as relying on the AI to not die is annoying even on recruit difficulty.

NOTE: Your aggrometer wont always fill up. Try killing someone with the turret and it should shoot up or get off the turret and sometimes the bar fills up itself. If you struggle for kills try using a more accurate weapon or a shotgun for maximum damage.

Update: Due to the server closures I recommend doing this in splitscreen COOP or you can 'try' with the AI partner.

Best solution is to start up "Aircraft Carrier". Enter the ship and you will get to a position with a riot shield. shoot out of the door to get the attention of the 6 enemies. kill one of them to get a full aggro meter. now run towards the enemies and kill them while in aggro mode. once all are dead kill your partner and start over from the last savepoint (at the riot shield). It is confirmed that you can just load up the last checkpoint to speed things up.