This achievement is for 10 captures of the npc character in submission gametype which is a territories variant.
This is easy to do with some patience. After 2 captures, one per round, the game will end. Therefore it takes a minimum of 5 games to get this achievement. But as other people go for captures too, this is unlikely. Tell your team you're going for the achievement and they may allow you to get it, or alternatively, play with a group of friends and take turns getting captures.
During the matches, rush for the meatflag and get him down. Grab him and make your way to the ending area, which moves when the other team captures it, and is random.
When dragging the meatshield, you are more protected than normal, and a good player can take down several attackers one at a time with the starting pistol and melee hits. The rest of the team should be scouting and protecting the rear to grant you safe passage, so if they aren't, tell them to.
Newer updates have allowed the option of unlocking this achievement in Social xbox live, meaning you can choose the submission gametype and have the match populate empty slots with bots. But apparently you will need all the available dlc packs to unlock this achievement via the social route.
They most likely changed it because the release of Gears 3 took away even more players, on top of the already low amount of people playing Submission.