To obtain this achievement you simply must kill someone who has a spree of 5+ kills IN CLASSIC matchmaking (Doesn't work in custom matches).
This is obtained by killing someone that is on a killing spree or greater, (5+ kills without a death in between). This will give you the medal Killjoy and unlock the achievement. It doesn't announce sprees so the best way to guess someone is on it is if they seem to be running around for a while without dying.
A few enemies you should target are people running around with swords, shotguns, try to kill them immediately, if they weren't on a spree at least you got a kill. Someone sitting the the back of the map or camping with a sniper can easily have a spree.
If you do know of them try to keep going at them even if you die, respawn and try again. Throw all your grenades every time to flush them out, or if you get a rocket, sword, shotgun, or sniper you can use that to kill them too.
If you plan on play this for a while don't go out of your way for this one it will come naturally. If you plan on getting the other online achievements you should go for this last because most likely you will get this on the way.
I got this in my 3rd RANKED Halo 2A team match.
Good luck and have fun!