To do this achievement you must start from the very beginning of the game and finish all chapters and acts to the end. It doesn't have to be done in one sitting, but each chapter and act must be finished (difficulty also doesn't matter). Also this must be done in co-op (local or on LIVE) and you must NOT be hosting
Follow the guidelines for the other Dom achievements and you will have this one in the bag easily, as well as these along the way:
The Dom-curious achievement in Gears of War worth 13 pointsComplete 1 co-op chapter as Dominic Santiago on any difficulty The Domination achievement in Gears of War worth 32 pointsComplete 10 different co-op chapters as Dominic Santiago on any difficulty
Note: Just like in Gears 2, the tutorial at the beginning of the game counts as a "chapter" so if you don't get the achievement after finishing the game, make sure and try and do the tutorial at the beginning of the game first, to avoid having to make a possible 2nd run through.