To leave Blackbeard's fortress you must:

Make an Authentic Pirate Drink
Defeat a Janizary Ambush
Fight and Kill Bone

Once you arrive at Blackbeard's fortress you can talk with Anne and Rockfish or just find that barrel and take the lump of coal. Head toward the elevator and move the lever to the middle level to go the the tavern.

You can talk to everyone in the bar to get more information on the story. Your ultimate goal here is to make a special drink to get Blackbeard to come down. The only other ingrediant you need is some sulfer which is in the big pot that Lyle is snorting. He will give you some and then you can go behind the bar to make the drink. The recipe is on the last page of the diary you found back on the island, but here it is again for easy reference:

Click on these items (order isn't critical):
- Rum once
- Salt Peter twice
- Coal (from inventory) once
- Sulpher (from inventory) once
- Syrup once
- Pepper Sauce once
- then move the mug under the keg and twist the tap twice
- Finally, stir this nasty mess with the spoon

Take the mug to Rockfish who will sample the drink then take it to Blackbeard if you made it correctly. You will now have a short conversation with some pirate in a flowery shirt. That ends when Blackbeard comes down the elevator to meet the maker of that special drink.

Talk to Blackbeard and listen to his tale. You will gain more valuable background information. Soon Blackbeard will passout along with everyone else in the bar. Seems Bone has tainted the Rum and now that everyone is asleep he is summoning a small band of Janizary. It's up to you and Rockfish (well mainly you) to defeat the invading army of robed assassins.

You must do battle from a cannon mounted on a mine cart which rides on an elaborate set of tracks which spiral around the entire fortress. You will stop at three different locations where you can pan about freely and fire on the enemy.

The first stop will have the assassins peaking out a caves and attacking from the mine cart tunnel as well as from the top of the cliff. They will throw bombs and daggers at you which you can shoot to deflect them and avoid taking damage.

The second stop is outside a warehouse area. The Janizary are hiding behind crates and at each side of the opening. Kill them all to advance to the final stage by the beach. Here, the enemy will attack from behind rocks and the wooden posts which make up the rail system.

After you have cleared all three areas you will be thrown from the mine cart and land on the beach where you must do battle with Bone. He puts up little resistance if you attack swiftly and mix up your attacks. When he is dead you will have some move conversations with Blackbeard and the crew before traveling to Cartagena.