I have the quest "Kill the bandit leader located at Nilheim". When I go there all the bandits are labeled as guards and are friendly to me. The quest marker is over the head of a guard in the tower. When I attack her she starts shouting stuff like "What are you doing? I'm on your side!" I hit her a bunch of times and I don't even think it's possible to kill her. Anyone know what's going on here?

Was I supposed to start this quest somewhere else? I got the quest when I discovered Nilheim through random exploration so I'm thinking maybe I was supposed to get the quest from a character somewhere else first...

SOLVED:
So I was kind of right, you need to start the quest by speaking to a specific character. He happens to be hanging around very near the tower, looking for eager adventurers like yourself. Can't quite remember his name (Traven maybe?), but he's a bow wielding wood elf and he asks you for help with Nilheim.

My problem with this quest is that I also found Nilheim and Telrav through random exploration, talked to Telrav, followed him into the camp, got ambushed, and killed all the bandits.

Now, fast forward to an in-game week or two later, I asked the innkeeper in Ivarstead for a job and he gave me the bounty to kill the bandit leader at Nilheim. I went back to Nilheim, and all of the dead bodies of the bandits I killed are still there, including Telrav. I did go into Nilheim tower itself and found another bandit still alive that I had missed on the first pass through, but after killing her, the quest is still active. When I use Clairvoyance with this being the only quest marked as active, all I get is a "No Active Quests" message. No quest marker shows up on the map, either at Nilheim or anywhere else. So yeah, this quest is definitely bugged.

(EDIT)

Okay, I was able to "fix" this by opening the console and typing "setstage BQ01 100". This made the quest advance to the next step of returning to Riften to collect the bounty. I just hope it didn't screw anything else up, as I don't care for messing around with the console unless I absolutely have to...

(/EDIT)

Another non-console option should be to wait outside the loading cell for it to reset / respawn and kill the Bandit Chief.