Before you start this mission, you invest quite a lot of money into upgrading the Jackdaw, if you haven't already. What you will find useful is the fully upgraded swivel gun; you should also make sure that you upgrade the heavy shot. It also pays off to increase the boat's durability and invest in the battering ram. You should also remember to replenish ammo. Also, make sure that you have smoke bombs on you.
The way is long and full of opponents. Surely, you can steer away from them, or ignore even after they have opened fire, by sailing ahead. Still, with the upgrades that you have bought, they should be no threat to you (as long as they do not outnumber you greatly) so, it pays off to smash several enemy ships along your voyage and fill the holds with valuable loot. After you seize a ship, make sure that you use it to repair the Jackdaw , if it is damaged, or dispatch it to your fleet if it is in good condition.
OPTIONAL OBJECTIVE- rescue five survivors
It is a good idea to rescue pirate survivors along your way, to complete the optional objective. There is a lot of them so, gathering five should not be too difficult.
The Blackbeard's galleon can be found moored in the nearby harbor. Sail there and then, run ashore.
OPTIONAL OBJECTIVE- kill three guards stunned by the smoke bomb
Defend Blackbeard against the attacks of the nearby soldiers. If you use the bombs, this should be very easy. Simply, throw the bomb and kill enemies. If necessary, repeat until you succeed. Remember not to waste bombs on one or two soldiers. Instead, throw them when there are 4-5, especially if they surround Teach. After the fights finish, loot the corpses and when you are ready, go aboard the Blackbeard's ship to face the enemy ship.
Watch out for the enemy ship's mortars, approach it by sailing towards its bow and shoot chains at it to slow it down. Position yourself at an angle of 90 degrees, relative to the enemy ship's bow and stop. Ram it whenever it comes close Even if it approaches you and you collide, the damage is not going to be too significant, which you can tell by the above screenshot. The ship blocked this way should be pounded with successive salvos strengthened with shots into any available weak point. The enemy's fall is a matter of several moments then. After the cutscene, jump onto the enemy ship and kill the captain by surprise to complete the mission.