The Level 13 Black Pearl quest starts in Novigrad, but quickly takes you to Skellige for most of the story.

To start the quest, head to the The Golden Sturgeon Inn in Novigrad. Talk to a man named Nidas to learn about his hunt for a special black pearl, which he wants to present to his wife.

Fast-travel to Skellige -- you can head to Arinbjorn and jump across the gap in the bridge or head south from Eldberg Lighthouse . If you haven't been to the west of Skellige yet, pick your closest waypoint and head to the narrow peninsula all the way on the western coast.

Talk to Nidas on top of the broken bridge. Follow him until you get to the shore near the oyster bed and he'll ask you to go dive for the black pearl. While underwater use your crossbow to fend off any attackers. Once you find the oyster bed use your Witcher Senses to find to find the oysters.

As you swim back to the shore, you will see Drowners attacking Nidas. Take out the Drowners and give the pearl to Nidas. Nidas informs you that he didn't bring any coin and asks you to collect your reward at The Golden Sturgeon. Fast-Travel to Hierarch Square in Novigrad and make your way to The Golden Sturgeon. Once he gives you the coin, ask him about Letta.

You find out that Letta is sick and can't recognize her husband anymore. Unfortunately, even the black pearl couldn't restore her memory, or even put a smile upon her face.