Play and win 25 matches of Team Deathmatch. Team Deathmatch pits 4v4 with a finite amount of lives. In social or competitive matches the number of lives is 10. Once a team exhausts their 10 'extra lives' they will be down to their last spawns. So the team to bring that number to zero, and kills the remaining players on the map, wins. This will come eventually if you put in enough time and effort. You can complete this in Social or Competitive matches; or a mixture of both.
Even though the achievement description does not say specifically "social or competitive", this can NOT be done in private matches; it's been tested.