You need a streak with 4 wins in a row BUT you can use an exploit to make your life a lot easier.
If you are about to loose a match, quickly press the Xbox button, go to your dashboard and close the game completely. When you are quitting out this way, it won't count as a lost game and your streak is not broken. Now proceed as usual and set up a new game.
I just got my achievement this way. After a win we were about loosing and restarted the game with the method above, got three wins in a row and the achievement popped.
Furthermore we were able to matchmake with friends (I can't promise that this will work for you too, but it's worth a try):
Split up ingame 2 vs 2, highlight the Showdown matchmaking on your ingame phone and search at the same time. We matched up after your third attempt. (Done on a weekday evening with all of us comming from the same country). You stay together after each match, so you can get your four wins within 10 minutes.