Daily Objectives were introduced in the Heists Update. They unlock at Rank 15 and players receive GTA$ and RP for their completing.
To complete this daily objective, you need to participate in a team deathmatch. The type of deathmatch is important because there’s another daily objective for a regular deathmatch.
Go to the pause menu, choose “Online”, “Jobs”, “Play Job”, “Rockstar Created” (not necessary), “Deathmatches”, and then choose any deathmatch where two players are enough.
Set the type as team deathmatch. To complete this objective as quickly as possible, set 5 minutes time limit, 2 teams, and 10 kills as the target score. Confirm settings and invite at least one player to the job. If no friends can help you at the moment, set the matchmaking option as open, run auto-invite, and wait for random players to join.
You can also try to find a deathmatch using the Quick Job option or accept an invite (how to do that: Jobs in GTA Online). However, in this case, you will not know a type of the deathmatch in advance. To complete this daily objective, you need strictly team deathmatch.
The outcome of the deathmatch doesn’t matter. The main thing is to complete the job because this daily objective completes after it’s ending. If other players quit the job, this will not affect you negatively.