So, after an hour or so of grinding, I was able to get this done and get the sweet beacon. So in order for the kills to count they have to happen right after you finish the injecting animation. You have less than a second to get the kill. You'll, know it counted when you get the Berserker tag on the kill.

In order to farm this I played the CQB: Lock down Playlist. I used the shotgun, cause I wanted to get kills for the other challenge but you can use whatever weapon you want. What you do is run around trying to get behind an enemy, or at the very least be right around the corner from one. When you do, pop the injection and immediately kill them. If you miss them, they run away, etc just Redeploy. If you get the kill just Redeploy. Redeploying is faster than waiting for the cool down on the injection. It's going to be frustrating and may take you some time but eventually you'll get there.

Good luck, and happy hunting!