These count across all your playthroughs on any difficulty and it doesn't matter if you are in co-op or solo. You can check how many of these kills you have by going into My Page > Statistics > Campaign Statistics. They are listed under "Enemies Defeated (VSs). Unfortunately, there is no "total" for these stats, you will have to count each section across all difficulties to get a count. This will come pretty quickly. You can equip the "VS Takedown ability" which will help you kill them quicker. Also, blowing up enemy turrets count towards this. I got this achievement before the end of my first playthrough.