This is an entirely stealth mission and a perfect mission for you to practice your blowpipe handling. The blowpipe allows you to use Sleep or Berserk Darts silently. The number of darts and the duration of the effects can be upgraded by crafting. Sleep Darts will temporarily put your target to sleep, giving you enough time to pass by him undetected or get close enough to kill him. You can also use these to get the attention of nearby guards as they'll check out the target. Be warned though that the target may wake up faster because his comrades will be waking him up.
Berserk darts are perfect for diversion and best used on those huge, bulkier enemies and elite officers. The target will attack ANYONE nearby while the dart is active. Fortunately, the target will also die from exhaustion once the dart's effect expires. Take note that an actively berserk target will notice you immediately and ruin any stealth-related optional tasks you're trying to accomplish so stay out of sight of those you set to berserk.
Start off by putting the first guard to sleep. Once he's down, Kidd will go down and finish him off. Loot the bodies of the enemies you targeted with your darts to recover your darts sometimes. The prisoners you'll rescue have guns pointed at them. These trigger-happy guards that will shoot the prisoners instantly in the first sign of danger. Climb the nearby wall and take out the gunner first. Next, kill the lone guard on the ground to the southwest to free the first prisoner and find a chest as well.
Climb back up to the wall then go to the prisoner to the west, inside a temple ruin. There you'll find another chest and the prisoner as well. Take out the guard the way you prefer to. Next, use make the gunner on the ground go berserk and let him to kill at least one of his comrades. Once done, you can now go and use a sleep dart to divert their attention or perform a double-assassination. Release the nearby prisoners as well.
Circle around to the ruins to the north to find another lone guard with a prisoner. Eliminate him away from the view of his comrades and free the prisoner.
Now you'll find two prisoners with gunner holding them. Quietly eliminate the standing guard behind the gunner while the two patrols are away then hide the body in one of the nearby bushes. You can then use a berserk dart on the gunner to make him engage the patrols or take your time taking him out covertly.
Free the two prisoners and synchronize with the nearby viewpoint to fully reveal the island. The temple entrance under the viewpoint leads to a closed door holding the Mayan Outfit that is also marked in your map. You can't access it yet at this point so leave it for now.
Head to the north then kill another single patrol then free the prisoner. Scale the nearby walls to reach an upper path where there's another patrol you can eliminate. Tread the downhill path and turn left to find the last chest behind the foliage.
Continue heading downhill and you'll spot two more guards. Get rid of them then proceed to the nearby prisoners. Move to a good vantage point then use a berserk dart on the gunner again when the patrol is nearby so they can go ahead and kill each other. Once done, assassinate the survivor(s) and free up the prisoners immediately. Be careful when doing this since the gunner in the nearby tower can still spot you.
Move to the northeast and hide behind the bush beside the tower so you can pull the lone patrol there as soon as he passes by. There's also another prisoner on top of the nearby guard tower as well so climb the nearby tower then quickly take out the gunner. Release the prisoner afterward.
Move around again to the northeast using the concealed path to the north. Carefully get near the next set of prisoners. Use a berserk dart on one of the guards, let them kill each other then take out the last one. Rescuing the next set of prisoners to complete your target number. A cutscene will trigger shortly.
During this scene and after speaking with Kidd, the assassin contracts around the region will be briefly revealed. The next story-related mission is in Nassau. Before going there, get the last collectibles you haven't collected in the area.