To start this quest, you must revisit the Assassin headquarters in Tulum and talk to Adé. This will become available after you complete the Delirium quest.
Edward returns to the Assassins to made amends for the damage he did years ago, and finds a ripe opportunity to help.
Simply follow him toward the ruins. Once you arrive, Ah Tabai will be informed of another soldier attack on the Assassin settlement.
Run after Ah Tabai toward the beach. Don't fight the soldiers you pass - the other Assassins will handle them. Shortly after, you'll reach a hill overlooking the beach where Assassins are fighting the soldiers.
Hint:
Jump down to the beach and, using whatever methods you prefer, help the Assassins get rid of all the soldiers on the beach.
Hint:
After getting rid of all the soldiers on the beach, you must kill the enemy ship's captain. There are some riflemen on board the ship. To avoid their gunfire, quickly get into the water and swim below the surface.
Swim to the other side of the ship, climb up the side, and try to scale the rigging to one of the masts unnoticed.
Wait until the captain, who keeps moving around the deck, is within reach, and take him out with an air assassination.
Once the captain is dead, this quest will end, unlocking the next main quest - A Governor No Longer - as well as an additional side quest added in the Resynced version - That Bastard Maynard.