To get this achievement, you must kill 9 unique players that have the Serial Killer achievement. You do not have to be a Serial Killer yourself. Multiple kills on the same player will NOT count. Kills count in any multiplayer mode.
If you have time in a lobby, look up the achievements of each player quickly so you know who you have to kill. It's a good idea to try and kill every player in a game at least once if you do not have this option. If you run across a random still playing this game, it is likely they've played enough to be a Serial Killer.