The page below of the Assassin's Creed III Remastered contains a walkthrough for Captain Kidd's Treasure - Dead Chest's Treasure.
This mission will be available after you collect six Peg Leg Trinkets and bring them to the man at the port.
As you reach the shore, climb onto the nearest rocks and jump from them onto the wreck on the right.
That way you will reach a small beach from where you have to climb onto the cliff on the left.
Optional objective: Perform three kills while running.
Optional objective: Don't let the target get away further than 40m.
Optional objective: Complete all optional objectives during a single playthrough.
Move along the rocks right and left and eventually you will reach an abandoned wreck which is being searched by a thief.
The man will find the piece of man which Connor is looking for and you will have to get it back. Chase the thief, jumping between the ship wrecks.
During the chase, you might come across single enemies. For full synchronization, you will have to make sure to kill them while running. To do that, just keep the free run button pressed and press attack.
Optional objective: Kill the runner before he reaches the cave.
At some point you will find yourself on a falling mast. Be ready to use your firearm to kill the enemy before he manages to reach the cave. In the cave itself you will have to fight a group of enemies, killing whom will end the mission.