This achievement requires you to win any multiplayer mode game ten times. These games can be Deathmatch or Team Deathmatch but they cannot be private match.
Luckily they can be boosted. Search for a game and hope that it creates a new session. If not let the game you are in begin, leave the game, then search again. This might net you a new lobby, allowing your friend to join in. Both of you need to ready up and the game will begin. Deathmatch takes 15 kills to win, Team Deathmatch takes 50 kills to win.
A good way to continue getting 2 player games is to get one to begin with, then when that match ends, search again immediately. This will match you in a 2 player game again most of the time.
There is a HUGE glitch going on in this game online where if you join a game and it starts, but you leave and search again, it will place you in the same lobby but you can't ready up correctly because the game is in session. The only way to fix this is to wait for that match to end. This has also caused Xbox freezes.