This must be done in Escalation matchmaking, can't be done private matches.
Your two options are to either play ranked Escalation under "COMPETITIVE MODES" which may be harder depending on your current rank and your actual skills in the game or you can play the new special playlist that has no ranking that they added just this weekend with the three days left of the challenge to go. The only thing special abut this version of Escalation is that it will fill with bots and I believe it has increased XP gains but because of the lack of ranks, it should be much easier as really bad players can possibly end up on the enemy team or you can play with really good players that wont automatically match up with other really good players.
Regardless of which mode you choose, depending on your luck and skill this shouldn't take you more than a few hours.
Just remember you only have to win rounds and not full matches. So you could possibly clear this in seven matches as each match is first to seven or it could take you slightly more if you only win a few rounds every match.
When you get this done, don't forget to claim your reward by logging in to this site:https://gearsofwar.com/en-us/my-rewards
You'll get two Snub pistol skins for getting the Challenge achievement and one of them will give you credit towards this achievement if you haven't already unlocked it: