Park outside in the boat and swim over to the beach in front of the cave. Look to the right of the entrance for a message in a bottle (5). Run over and enter the cave. Follow it through until you reach a large cavern with a natural hole in the roof letting light in.
Climb the wooden platform immediately to your right and dispatch the Gunner. Drop down to the wooden walkway below and look out for the first ladder on your left. Climb down here and look behind the wall at its base for an Animus Fragment. Climb back up the ladder and follow the walkway all the way left. Kill the guard at the end. At this point, loot the nearby chest.
Drop down the ladder at the end of the walkway and eliminate the two smugglers standing by the campfire in the camp directly ahead of you. Loot the chest up against one of the tents here. Continue towards the wooden docking platform beyond the camp. Eliminate the three bad guys here.
Once it is all clear, there is a third chest to loot on the ground level of the docks hidden behind some crates. The final chest is on the higher level of the docks that we can climb up to on the eastern wall.
Drop down into the water and swim below the platform that housed the final chest to find another Animus Fragment. Now that we have everything, we can exit the area.