This quest begins automatically after completing "The Sage's Buried Secret" quest, when Ah Tabai informs you that some of the Templars as well as your crew have been captured by hostile soldiers.
Edward must save his imprisoned crew and various captured Assassins from the slave traders that have arrived in Tulum.
At the beginning of the mission, you will receive sleep darts from Kidd. You can use them to put enemies to sleep. Sleep lasts for a limited amount of time and sleeping enemies draw the attention of other enemies due to their strange behavior.
Put the guard in front of you to sleep, and while Kidd finishes him off, jump across the branches to the nearby ruins and kill the marksman.
Shoot a sleep dart at the soldier who is about to shoot one of the assassins. His strange behavior will draw the attention of his companion and another guard standing a bit further away.
Move onto the tree and wait until they enter search mode - then hang two of them and kill the third with an air assassination. Once you've done that, approach the prisoner and free him. This is the first of nine prisoners you need to free.
Head north and take the stone stairs to the right. Use Eagle Vision to check the current position of the guard patrolling the area, and when the opportunity arises, assassinate him stealthily and free the second prisoner.
Retreat back the same way you came, roughly to where the first prisoner was. A little lower, looking east, you should notice two more prisoners and three soldiers. First, sneak up to the one standing furthest away and assassinate him. Next, approach the two standing near the prisoners. They are standing too far apart to use a double assassination, so shoot one with a sleep dart, quickly assassinate the other, and then finish off the sleeping one.
Those are all the prisoners on the upper level, so use the nearby viewpoint and leap into the water below. Once you get out of the water, you should have two soldiers in front of you guarding two more prisoners. Sneak up to the one standing in the back and assassinate him. Next, do the same to the soldier standing closer to the prisoners. If you do this quietly, two guards standing a bit further away will be taken out by friendly assassins. Free the two prisoners.
The next prisoner is a bit to the right. However, start by climbing the nearby watchtower and killing the marksman on guard duty.
Wait in the bushes at the foot of the tower for the soldier patrolling the nearby paths, lure him into the bushes with a whistle, and assassinate him. Next, go around the huts and, in a similar way, assassinate the soldier standing to the right of the prisoner. Then approach the soldiers standing near the prisoner from behind and perform a double assassination on them.
You'll find the next prisoner by heading toward the coast. You can approach the soldiers guarding him from behind and perform a double assassination on them.
Head back toward the watchtower and cross to the left side along the large branch. If you want to move across the rooftops, you should take out the marksman on the second watchtower.
Of course, you don't have to go over the roofs - you can also move between the huts a bit to the east, as that's where you'll find the last prisoner. Deal with the soldiers guarding him in whatever way you like and free the prisoner.
On the map screenshot below, I have marked all the locations where you can find the prisoners.
James Kidd is waiting for you near the coast, not far from where the eighth prisoner mentioned above is located. This will trigger another cutscene.
Talk to James Kidd to unlock a new feature - Assassin's Contracts.
Follow Kidd, and he will lead you inside the Mayan ruins where a mysterious door is located.
Simply interact with the door to insert the first Mayan stone that you acquired earlier, during the quest This Old Cove. This will end the quest and unlock two more - one main quest - The Forts - and one side quest - Mayan Mysteries.
