UPDATD: I was wrong about this. I tried it again on my Titan and it didn't work. I'm not sure what happened the first time but I definitely didn't kill the boss.
Original post:
The mission description says to clear all of the enemies but you don't need to do that at all. In fact, you don't even need to kill the boss. You can just run past all of the enemies (top tree Nightstalker on Hunter makes this super easy) and open the boss chest to complete the mission.
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2 RepliesThough killing the boss is what allowed sector chests to be opened in the first place.