This world's story takes place during the events of the motion picture: Pirates of the Caribbean: Curse of the Black Pearl with a few differences. Including those minor differences are the appearance of Heartless a bit everywhere in the world and an Organization member, Luxord.
Story of this world
Sora and his companions arrive in Port Royale and meet Jack Sparrow, who informs them not only is he trying to get back his vessel the Black Pearl, but also rescue Elizabeth Swann who was kidnapped under the orders of Captain Barbossa. On there quest, Jack will team up with the group to fight undead Pirates. This new party member will help you do additional attacks. Later when encountering Barbossa, he demands that Sora passes over Elizabeth's Medallion (he obtains it during playing through this world). Then a fight will start between Barbossa and Jack . Although, even after obtaining the Medallion, Barbossa doesn't let Elizabeth free. Regardless of those statements, we later see her safely in the hands of Will Turner.In this world we also meet a member called Luxord, here to stop Sora. You will have to defeat him as well.
This world has an interesting mechanic as you can only hit enemies if they are under a moonlight spot which makes the game more challenging and fun. The best ways would be to bring the enemies next to the light and start your attacks for the final blow to hit the enemy when he's under the moonlight.