Biddle's Hideout is a naval mission in which you'll be leading your own ship. The chapter below of our Assassin's Creed III Remastered guide contains a walkthrough for the mission.
Optional objective: Take out the mast of the main ship in one chain shot.
Optional objective: Take out the Man of Wars in the time limit 3:00.
After the mission begins, swim between the rocks to the left, following the ship.
Soon afterwards you will be attacked by two more ships from the right. Start the fight by going half sails and destroying the masts of Randolph. For full synchronization, you need to land a perfect chain salvo. Take into consideration the enemy ship's speed and how the cannonballs' flight path. The optional objective requires that all of them hit the enemy.
With Randolph immobilised, move on to the other enemies. You have to destroy them in 3 minutes and move on to boarding the ships. This might prove very hard if you haven't upgraded your ship properly. Most of all you should buy the heated shot so that you can destroy enemy ships fast. It's best to get nearby an enemy, pass by him and shoot a full heated salvo.
After a successful attack, a white ring should appear on the enemy ship, pointing to the gunpowder storage. Shoot it with the swivel guns to sink the ship.
Optional objective: Only kill Biddle.
With both of then sunk, sail to the previously immobilizes ship and board it. Don't bother fighting, just run straight to the captain.
To defeat Biddle, press the jump or counterattack button after each successful block and afterwards hit him a couple times while he's out of balance.
Follow the same tactic below deck and you should end the mission fast.