You need a minimum of 4 people. Get yourselves into an Xbox Party and all search for the same game type and if the servers aren't too busy you should all be grouped together. If not you can invite people in. If you keep to the same sides its easier to follow. You need to do 2 games of TDM, Cry for help and Rescue and one game of FFA for each person in the group.
Start a game, and then as soon as you are all in one team should exit the game. The other team will win by default. Repeat for the same mode before moving to the next, obviously the team that backed out first stays in the second time.
For FFA the group need to exit the game except the player that will be the winner. Repeat for everyone and then the Achievement should pop.
You can check the status of the achievement in the TR menu "Feats and Setbacks" which shows what games you need to win. Useful if the achievement doesn't pop for you.
The matchmaking seems a bit ropey on TR so in between each game everyone should back out to the game menu. This seems to ensure that people are finding a lobby quickly.