The immortal bar patrons in Night of the Comet. They're immortal. You can't kill them.
This is a known bug. It's been known since may- possibly even before.
But it hasn't been fixed- now, maybe it's not top priority to fix a bug that will absolutely ruin the game experience for new players by preventing them from completing a mission that is needed to unlock the next set of missions- and thus from advancing beyond that point.
But if it isn't- (as is obviously so), I think the question to ask is: Why?
Again, this is a known bug. There's no excuse for not fixing it, especially with the change to how missions operate. Before you could just never finish that mission and go on to greater and better things. Now you can't. Seems to me like the constant platitudes of "We have other things that need attention" need to go away, and you need to fix this bug.
EDIT: I've submitted a ticket # 17,021. I've also submitted other tickets before, but I don't remember their numbers- only that you refuse to fix this bug.
I experienced this bug several times yesterday on Tribble and although this bug has existed on the Live servers for a while now, I noticed the way to circumvent the bug is to take out the Klingons and Federation bar fighters in the room prior to taking out the dividians in the bar, 9 times out of 10 this completes the mission regardless if any of them go invulnerable or not... Taking out the dividians in the bar first, tends to be a roll of the dice as to if the mission will get stuck or not...