There are many ways in which you can activate this quest.
1. Arx - Sewer's entrance
2. Arx - wedding
You can do that by discovering a warehouse full of Death Fog crates in Sewer .
If you also use Spirit Vision then you will be able to speak with a thief's spirit. He tells you that he saw a royal guard in this area.
However, if you went to the wedding first  then you can interact with the cake. It explodes and at the bottom of it, you can find a letter from the Doctor. There is also a statue that spreads Death Fog.
The goal of this quest is to find Justinia, the queen of Dwarves. She is in Isbeil's hideout. You can access that place by going through Sewer. There are secret doors that are opened by pressing bricks in a wall.
You can open them if you have at least 5 points in Thievery. If you don't have this much points then you can use a key that is inside of a room with spider webs near a Source pond.
Enter the hideout. You can see the Dwarven queen. It turns out that she was manipulated by Isbeil. You must fight Isbeil regardless of which dialog options you chose. However, you must be tortured first. It doesn't matter what you do because you won't receive any damage.
Win the fight and go to Isbeil's laboratory. There, you can meet with the queen. Speak with her and decide about her fate.
Choice 1: Kill the queen
You can decide that the queen doesn't deserve any mercy and she needs to die. She will fight you. The queen is alone so you shouldn't have any troubles with her.
Reward: 149,850 experience points
Choice 2: Spare the queen
You can decide that the queen isn't guilty and can go. Showing her mercy gives you a reward.
Reward: 4 guaranteed rewards + 1 out of 4 to choose from depending on your character's class