Assassin's Creed 4: Black Flag Walkthrough Part 79 Shipwrecks & Caves: “The Black Trench”
From the Diving Bell you are going to want to head straight South into the wreckage in front of you. Favor the right-hand side to reach the first chest. After that just keep going forward until you can enter a patch of sea weed. Keep low as there are sharks in the area that will attack you.
Once in the seaweed patch, you will see a nearby air barrel, use it. Go into the wreck just next to the seaweed. You will find a treasure chest there. Now Go to the edge of the wreckage and turn to the right. Duck into the Seaweed and wait for the shark to move away from you. Swim up the slope and duck into another patch of seaweed. Wait for this shark to turn away from you then go into the hull of the ship. You will find a chest in there toward the bow of the ship. Collect it then return to the area where you got the second chest.
Now continue to the bigger piece of wreckage, the captain's quarters. Now you want to hit one of the air barrels. The first chest inside this part is just ahead in the very bottom of the area. The second chest is a bit trickier. Swim up through the hatch above you then look down toward the stern of the ship. There you will see the chest. After that swim upwards to the deck of the ship.
This next part takes some intense timing. Wait for the sharks to be moving away from the center of the deck. Swim up to the next opening in the deck and go inside to find the first Animus Fragment. Now lunge on up toward the Air Barrel above you. Now watch the shark below you. The moment its patrol goes to your right is when you want to make for the second half of the wreck.
Once inside the wreck, go over to the right-hand side of it to find the sixth chest. Now use the air barrel sitting on the left-handside of the area. Head through the door just to the right of the air barrel. Follow this to the stairwell you will want to follow up. Go against the deck to the left and through the door to find a small room. Turn right and look down to find the final chest. It has the Design Plans for the Flower Sails. Grab them. Now you only have 1 Animus Fragment to go to complete this. Pause and grab some air from the nearby barrel if needed. Aside from that just make a straight line back to the Diving Bell to return to the Jackdaw.