This achievement is very easy and there is no need to play any of the new "Ultor Exposed" mission (though you DO still need the DLC). First up, you need to be able to play over Xbox Live (Gold account or Trial) and must have at least one other person to play with (be it a friend or a random).
To set up a Party Game, from the Main Menu, go to Xbox Live>Create Party. Once the lobby has loaded and you are in the match settings screen, you have to press "X" to switch the game to Party Mode. This mode is pretty much a Player Match mode but you get to pick all sorts of options, such as the time limit, kill count, infinite ammo no/off etc. When ready, invite at least one person to your game and start it.
You will receive the achievement as soon as the match starts and there is no need to finish the match. This can be done in any game mode (Strong Arm, Gansta Brawl etc.).