Your next obstacle requires you to avoid being eaten by sharks. Move left or right to avoid the rock pillars, then move left when you reach the fork. Keep swimming until you reach the current. When you reach the air pocket, lunge upwards to replenish your air supply. Once you open the chest, the place crashes down on you and you need to swim through the cave to get out. When you reach the ship, interact with the hull and dive in to find the chest with the medicines. If you touch one, it inflicts damage, just like real life. Swim over to the ship, but watch out for jellyfish. Dock to initiate the diving bell sequence. Meet up with Blackbeard's ship for another cut scene, then sail just a bit farther to reach the shipwreck. Once you have the diving bell, fast travel to Salt Key Bank or Havana to cut your travel time to the mission location. They run 5,000R from any merchant, or from the Jackdaw upgrades in the captain's cabin. You need to purchase a diving bell if you haven't already. When you arrive in Nassau, follow Blackbeard.
Use fast travel to get there, or take your time and plunder a few ships along the way. Return to the ship and set sail for open sea.