Can be done solo (Instant Action) or in multiplayer (Ranked or Private match)
If you do it in a Private Match with a friend, then have your friend Free Spawn in front of you after you are deployed. Stand beside your friend and run away from him and from the moment you go into overdrive mode, stop running and turn around and shoot your friend until he is one shot away from dying. Now run at him. You should hit the overdrive mode a few feet before you get to him and you will kill him instantly. Rinse and repeat 4 more times and the achievement will pop.
You can also do this with bots, but it may be somewhat harder. If you do attempt it with bots, remember that as long as you are running then it will hurt them, so if you miss the first time, do a U-turn and keep trying to hit him. Can only be done on enemy bots. Enemy bots on Trivial difficulty take about 2 hits to get killed by colliding into them in overdrive.