Step 1: Use a broadsword to defeat the Navy guards at once.
Step 2a: If applicable, equip a Revenant cannon ram to quickly destroy the drawbridges without using up your ammo.
Step 2b: Maximize the following skills for your gunning needs.
Step 3: Sail up close by the drawbridge outposts so the black pearl doesn't take too much damage to its hull. The enemy shots would just hit directly to the top of the ship and its sails which helps mitigate damage taken but sometimes they miss or hit the sides by chance.
Step 3b: Angle the ship slightly parallel to the bridge so you'll get a shot at one or two of the outposts using the cannon next the the wheel.
Step 4: Now equip the Steel Cannon Ram to increase damage for your broadsides (also adds a critical chance, The Black Pearl fires with only Round shots)
Step 4b: Circle around the Goliath and fire away. It can't hit you while you maintain your speed.
Step 5: Celebrate your victory!