This particular challenge is for playing through and completing 10 matches in either Brothers to the End or Social TDM. Social TDM is found in Social Quickplay and must be voted for. It does not always show up as an option in voting.
If you would like notifications for upcoming challenges or achievements for Gears 4, feel free to join the leaderboard I have made previously for the weapon skin achievements. The below information is posted over from my other solution.
Any other questions, feel free to comment or shoot me a PM.