This quest unlocks after completing the quest "The Gunpowder Plot". To start it, head to the beach located in the north of the island and talk to Vane.
Edward decides to assassinate Peter Chamberlaine before the Commodore can issue his orders to sink the pirates' ships.
Hint:
Follow the captain and the two accompanying soldiers. You can do this by jumping across rooftops, or you can simply follow them on foot - just keep a safe distance. Following them will lead you to Chamberlain's mansion, where the captain will talk to the soldiers guarding the estate for a moment before stepping aside and standing next to the estate wall.
If you were too far away during this conversation, you will need to get the letter the captain is carrying. Sneak up to him along the wall and assassinate or pickpocket him. None of the soldiers patrolling the estate grounds will notice that. Then, loot the Letter to the Commodore from his corpse.
Hint:
You can get onto the estate grounds in several ways. For example, you can go around the right side to the back of it. There you'll find a fallen tree trunk you can use to climb higher. Before you do, though, take a look around - there's a crocodile swimming nearby.
You need to reach the window on the upper floor of the mansion. Once you climb up the fallen log, head left right away, jump over the fence, and hide in the tall bushes.
Then climb the ladder, cross the roof and get in through the window. There's no one inside, so you can do it without worry.
Inside, you need to examine three clues in any order. The first is a letter lying on the table.
The second is a map pinned to the wall.
You also need to listen in on the conversation behind the closed door.
Hint:
Start by leaving the estate. Climb out through the window you came in by, turn left, cross the roof onto the balcony and drop down onto the estate wall, then move away from the estate grounds. If you do this quickly, none of the guards will have time to catch aggro on you.
The search area that will be marked on your map is fairly large. The camp you are looking for is located on the beach in the southeastern part of the island.
By sticking to the roads and paths, you can get really close without entering any restricted areas. Approach the beach from the western side.
Taking on all the soldiers and the commodore himself in open combat is a bad idea. The good news is that you only need to get rid of four guards to take the commodore out with a single, lethal strike. To put this plan into action - move a little to the left and hide in the haystack.
At the right moment, whistle to lure over the soldier patrolling this part of the camp and assassinate him.
Move to the right, sneak up on the two soldiers sitting by the campfire, and double assassinate them.
Hide in the bushes ahead of you, wait for the guard patrolling the right side of the camp, and assassinate him.
Wait for the right moment so you are not spotted by the soldier patrolling the beach a bit closer to the water on the left side, climb onto the tent where the commodore Peter Chamberlaine is standing, and air assassinate him.
If the commodore falls dead, you don't need to worry about the other soldiers - a cutscene will start automatically, after which this quest will end and the next quest - The Fireship - will automatically begin.