This quest is unlocked after completing the Imagine My Surprise quest. To start it, you must sail to Africa. You will find a marker on the eastern edge of the map that allows you to do this - sail up to it and interact with it.
Eager to earn the Sage Bartholomew Robert's trust, Edward offers to kill the two Templars, Burgess and Cockram.
Head toward land - after a moment, five Portuguese ships will block your path and attack you.
The ships you must face are a Frigate, a Brig, and three Cutters. You have to sink them all. The bay is relatively tight and features several rocky islets - be careful not to hit any of them in the heat of battle.
Once you get rid of all enemy ships, drop anchor at the designated spot, right next to the Princess.
A single path leads inland from the beach. Three guards stand at the start of it - you can, of course, fight and kill them, for example by shooting an explosive barrel standing near them, but it will be easier to sneak past them by moving to their left, where there is a ramp you can use to climb into the treetops and move forward along them.
On the other side, a soldier stands near a pile of palm leaves, periodically approached by another soldier patrolling the path. Wait for the second soldier to walk away, jump down into the leaf pile, and pull the first soldier inside. You can wait for the patrolling soldier to return near the leaf pile and do the same to him - but it is not necessary, as long as he does not spot you when you move forward.
After getting rid of the soldier(s), head up the path inland. You can sneak past the next soldiers by moving above their heads. Once you reach the gate, jump over it to the other side - a cutscene will trigger in which you meet the Sage. This time, he will decide to cooperate.
Continue up the path until you reach the Portuguese camp. Turn right before the gate and walk along the fence - after a moment, you should see two soldiers. Kill them. For example, you can hit one of them with a sleep dart, assassinate the other, and then finish off the sleeping soldier.
Climb up the tree trunk, jump over the fence onto a tree growing on the other side, walk along its branches, and jump onto the wooden platform on the other side.
There, you will find a note revealing that Burgess is somewhere near the docks.
Hint:
Now you must make your way to the east side of the island - that is where the docks are located. You can do this in many different ways. I will describe one that, with enough caution, requires no further kills other than Burgess and Cockram.
Turn right. Make sure the soldier patrolling the area near the tree you jumped over earlier isn't looking in your direction then drop down and head forward behind the small, yellow building on the right.
Move along the right side of the hay wagon to the bushes behind it. A soldier is sitting next to the wagon on the left side, but he isn't a problem - he won't see you. However, watch out for the soldier patrolling the area to the left of the wagon. Wait and move forward once he starts walking away from the wagon.
Keeping in mind the soldier patrolling the area - the one approaching the hay wagon - and especially the marksman on the roof of the building you are currently next to, cross to the other side of the path, go around the left side of the wall where the fat soldier is standing, and hide in the bushes a bit further ahead.
Still keeping an eye on the marksman on the roof of the building, head straight down until you reach a wooden platform with a crane arm attached to it.
Burgess and Cockram are located in different parts of the village. The trick is to reach one of them - which will trigger him to move and meet up with the other. Once they meet in the middle of the settlement, you will have a limited amount of time to perform a Double Assassination on both of them before they split up.
From where you are, you can reach either of them completely undetected - we will head toward Burgess. Turn left. He is one of the soldiers you should see in the distance.
Head toward him across the rooftops - once you get close, he will begin executing two pirates, and when he finishes, he will head off to meet Cockram.
Without delay, retreat in the direction you came from and cross the rope to the roof of the building across the street.
Then jump onto the scaffolding next to the building on the left and hide behind the pile of planks. Be careful not to be spotted by the guard on the tower straight ahead. A tree grows nearby - Burgess and Cockram will meet beneath it.
Once Burgess and Cockram meet, climb up the planks, jump onto the tree, move onto the branch above them, and perform a Double Assassination. You do not need to worry about the other soldiers - a cutscene will trigger automatically.
You will spawn on the beach just a few steps away from Roberts. Simply walk up to him and wait until he finishes speaking. A cutscene will trigger in which the Sage promises to help you - after which this quest will end, unlocking the next main quest - Black Bart's Gambit.
