You must kill 4,000 foes to unlock this achievement. It can be done in any mode (co-op/single/Xbox live/local play) on any difficulty.
Please note you must do all 4,000 kills on one campaign/save. You can NOT do 3,000 kills on easy and do 1,000 kills on hard.
If you have NPC players I would suggest killing them off (by playing them and jumping off a ledge) or set the team to defensive mode.
The two best way to grind out this achievement is:
1. Mephisto's Realm mission (you can mission select it or once you get to it during regular play). Once in Mephisto's Realm there will be five areas that contain five "puzzles". We want the one closest to the Extraction Point. To make sure your in the right place the Book of Majernik says "Thy way shall be lit by the flames of impure soles". From there you can kill as many enemies as you want as long as you don't toss them into the lake of fire in the middle. Also note you can toss the enemies off the outer sides to work towards your Widowmaker achievement.
2. You can do this on the simulation disc with Asgard as the map. So you will be picking a versus mission like Ulik, Piledriver, or Crimson Dynamo. The asgard maps have unlimited respawns and there is NO REASON to kill off the main boss (unless you have not completed the disc yet). That's right all your kills towards your 4,000 kills, 500 enemies off a ledge, and kills towards costumes are saved even after the fail of the mission. So you can spend all 20 minutes killing and not worrying about taking out the main boss. Also note you can toss enemies off the ledge when you get to the bridge part to work on Widowmaker achievement however not everyone can toss enemies over the bridge's wall but I know stronger hero's like Hulk, Colossus, or Wolverine can.
On your journeys to unlocking The Ultimate Super Hero achievement you will unlock (if you have not already):
You can also unlock/advance in these achievements:
Also if you switch to different characters during this effort you can make great strides to finishing off your comic missions and unlocking costumes.