This quest begins automatically aboard the Jackdaw right after you complete "Not Even a Real Captain". Your task will be to track down Maynard's ship, which has set sail for Eleuthera.
Maynard has left Kingston for Eleuthera on the HMS Demolition, and has a Master Gunner who might be persuaded to join the Jackdaw.
HMS Demolition is anchored just north of Cat Island, so the easiest way is to fast travel to that location. Once you arrive, the area will be shrouded in thick fog.
As you get close, Maynard's ship will start to pull away, sailing quickly to the east.
Give chase to Maynard's ship. Shortly afterward, HMS Demolition will rendezvous with six other ships from Maynard's fleet - four Cutters and two Brigs. All the ships will start attacking you.
Provided you've upgraded your ship, smaller vessels shouldn't pose much of a challenge. If needed, you can board them and use them to repair the Jackdaw.
The man-o'-war will be your biggest threat. It'll constantly shell you with its mortar, or fire its broadside cannons if you get closer. Stay out of the amber zones on the water, brace at the right moment when taking broadside fire, and use every tool at your disposal to deplete his health bar.
Once you succeed, sail up to it and board it. As usual, you'll need to break the morale of its crew, which is quite large. Watch out for the marksman posted high up on one of the masts - you can take him out while climbing up to cut down the flag.
After the crew surrenders, a cutscene will play where you free the master gunner, ending this quest and starting the next one. If you haven't recruited Padre or Lucy to your crew yet, the next quest will be "Master Gunner, Shipwright, and Master-at-Arms."
