Contract: Muire Dyaeblen - Skellige
Location: Kaer Trolde Harbor
Quest Giver: Kaer Trolde Notice Board
Other Requirements: N/A
There are a few different ways for you to pick up this quest. You can get it from the Kaer Trolde Notice Board or by speaking with Bjorg directly. It'll also pop into your quest log if you happen across the quest area prior to accepting the quest. Assuming that you got the quest from the Notice Board as most people do...
First thing you'll have to do is speak with Bjorg (pictured above) who will send you to another part of town to speak with the other survivors of the Drowner attack. This will update your quest and mark two locations on your map, as shown in my screen shot below.
Note: The southern most quest circle by the cave entrance you see on my map below is an alternative entrance to the same cave. If you wish go in that way since it's easier to find.
Go to the circle just south of Kaer Trolde Harbor to find a few Drowners and a corpse glowing red on the shoreline. Inspect it to acquire a scent which you will follow through the water a bit to the south where it will go underwater. Dive in this area and you will see foot prints on the bottom - follow them through an underground tunnel to the Drowner's Lair.
Search all the objects that glow red inside the lair to deduce that it's actually a Water Hag's lair. However she won't come back while Geralt is inside, so you'll have to go into your Alchemy tab in your inventory, under Potions and craft Drowner Pheromones to mask your scent. Hide in the cave after crafting and using the potion until the Water Hag comes out.
The fight with Abaya is pretty simple, she will summon Drowners to attack you at the start of the fight, use Igni to light her on fire to deal a lot of damage to her and immobilize her. Focus on the Drowners before her. Once she is dead return to town to turn in the quest.
Water Hag Weaknesses: Northern Wind (Bomb), Necrophage Oil, Quen, Igni