When the mission Target Encircled states to "Beat the same player in a DM 50 times", how in the world are you supposed to beat the same player 50 times in 20 minutes?
Same goes for All-Consuming Wrath (Beat 50 players after they beat you in the same DeathMatch) and other such missions.
It's written like this:
Beat 50 times a player you've already beaten in the same deatmatch.
That's not the most articulate wording, but it's very clear. It simply means you need to achieve the Persecution bonus 50 times.