Eliminate the Gripper Queen from her nest in the catacombs.
Workers and Guardsmen are having trouble with Grippers in the catacombs of the Outer City. These dangerous creatures appear to be everywhere in those subterranean waterways. The Judge asks Scarlett to find and kill the Queen Gripper so she can't lay anymore eggs.
Scarlett will need a Lantern.
Scarlett should know the Beast Knowledge skill to harvest beacons from the Grippers she kills along the way. This is a good way to keep fuel in the lantern, and extras can be sold for 20 ducats apiece. See Joanne in the marketplace if she needs to learn this.
The catacombs can be entered through sewer pipes under each of the three bridges. From the the Judge's courtroom in the Outer City, the center bridge is closest. Go to the canal and down the steps of the nearest gondola station, which is near the central bridge. Just wade into the water and swim under the bridge to find an opening into the Outer City Catacombs.
(Click on maps to enlarge.)
Swim to the nearest ramp, walk up on the platform. Scarlett really has a choice of routes, circling around either left or right. If she goes right, in the room with the stairs, she'll encounter a couple of stray Assassins. If she goes left, she can enter the Nexus Portal found on my wall of skulls and collect some extra treasure.
A large, circular room holds the Queen Gripper's nest, protected by the Queen and five other Grippers. The center of the room is a pool of water, which will extinguish Scarlett's lantern. Stay dry. A good strategy is to isolate the Grippers and deal with them one at a time. In a group, if they surround Scarlett, they become very dangerous.
The Queen herself turns out to be immune to many necromantic spells, for example, Blood Toll, so don't save Mental Energy for that fight. The warhammer it is probably the most efficient choice, assuming Scarlett has mastered it, but it's important to attack from the rear or side, avoiding those lethal claws.
For completeness, Scarlett may as well return by a different route than she came, giving her a chance to collect more treasure along the way.
The Gripper Queen's Beacon can be used as lantern oil that does not deplete. Once Scarlett has the Gripper Queen Beacon, she can sell her entire inventory of fish oil and regular Gripper Beacons.
There is ample treasure lying around down in the catacombs. A girl's gotta eat.
(As you may infer from the "(Outer City)" qualifier to this quest's title, Scarlett will later be asked to deal with another Gripper Queen.)