These count across all your playthroughs on any difficulty and it doesn't matter if you're 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 (Soldiers). Unfortunately, there is no "total" for these stats, you will have to count each section across all difficulties to get a count. This should come fairly easy over time, I would worry too much about it. I got this achievement before the end of my first playthrough.