After you complete the Dungeon quest you can talk to the girl in the nursery and she will tell you about the troll in the parking lot. You promise that you will chase it away for her.
When you get outside you will see the marker on the map - just drop down into the trash pile and then head towards the marker to find that the Troll is a heavy hammer type - couple ways you can do those - either melee them and heal a lot or use your book-stick (shotgun) and rifle to take them out then deal with any runners as you must.
Once you have slain the Troll you radio in only to learn from Rupert that the heavy you killed? That was not the Troll! A Bruiser bursts out of the shed in the courtyard - THAT is the Troll!
Again you have two approaches - either try to melee and heal, or shoot the sucker - either way you need to find a corner to use as cover for when it throws at you!
After you kill it Rupert calls and asks you to meet him at his workshop - he says he owes you a massive debt and means to repay it! So head to the marker to meet Rupert.
When you meet him he tells you that you can pick anything you want on the house! You collect the Angel Sword - and loot whatever else you like - and that ends the quest.