Destruction of the Edinburgh Trader

The Battle of the Isla de Muerta was a battle between the Royal Navy, the cursed crew of the Black Pearl, and the surviving crew of the HMS Interceptor.

Stranded
""But why is the rum gone?""

- Jack Sparrow after Elizabeth had told him they would be rescued by the smoke signal created by burning the rum

After the destruction of the Interceptor, Jack Sparrow and Elizabeth Swann were marooned on Black Sam's Spit. The two escaped after Elizabeth got Jack drunk, causing Jack to fall asleep from the alcohol he ingested. She then burned the rum, food, and jungle on the island to make a signal fire, much to Jack's dismay.

Rescued
""They'll be no living with her after this.""

- Jack Sparrow when he first saw the Dauntless, perhaps indicating he felt something for Elizabeth

The two were rescued by the HMS Dauntless with Commodore James Norrington and Weatherby Swann aboard. Norrington agreed to travel to the Isla de Muerta to save William Turner from death, and to arrest the crew of the Black Pearl, as a wedding gift to Elizabeth, who accepted Norrington's proposal.

Arrival
""You planned this all out, didn't you?""

- Will after seeing Jack secretly keep one of the coins, after having Barbossa attack the British.

With the use of Jack Sparrow's compass, the Dauntless arrived at the Isla de Muerta, with the Pirates already inside the cave, preparing to kill Will to lift the curse. Norrington, Jack, and other Royal Marines were waiting on longboats for the pirates to leave the island after they lifted the curse.

Jack managed to persuade Norrington into letting Jack go alone in the cave, and have Norrington wait on the ship. Jack was to trick the crew of the Black Pearl into charging out at the Dauntless on boats, while Jack would ambush Barbossa, and would lift the curse without killing Will, while the crew of the Black Pearl will be taken down by the Royal Navy.

Jack interrupted the ritual just in time, and persuaded Barbossa to not lift the curse at the moment, and use the curse against the Royal Navy, and take over the Dauntless, but this was all a trick for Jack to get his way. Instead of using the longboats, Barbossa ordered the crew to go underwater, and ambush the Dauntless from below.

Incredibly Stupid
Elizabeth escaped the Dauntless after being detained by the Royal Marines for her safety. She managed to slip away from the Dauntless' cabin, and used a longboat to travel to the empty Black Pearl, and free the imprisoned crew of the HMS Interceptor.

The crew of the Black Pearl managed to sneak aboard the Dauntless, with the crew of the Dauntless being distracted by Pintel and Ragetti, whom were on a longboat, and posing as women. The crew of the Black Pearl managed to assassinate several Royal Marines, but were finally noticed when Pintel and Ragetti got in a little squabble, and revealed their curse to the Royal Marines, whom Ragetti shot his pistol at, knocking Gillette's hat off, towards the invading pirates. The battle then began.

Weatherby Swann noticed his daughter's departure, and when he went to leave the Dauntless' cabin to tell the Royal Marines, he saw the battle taking place, and locked himself in the cabin.

Back at the cave, Will was still being held hostage by Jacoby, Monk, and Clubba. Jack and Barbossa were talking about Jack's honesty, to which then Jack stole one of Monk's swords, tossed it to Will, who then freed himself, while Jack pulled out his own sword and began to duel Barbossa, while Will dueled Barbossa's men.

Full-Out Battle
At the Black Pearl, Elizabeth threw Jack the Monkey into the ocean after it tried to scare her off. Mallot and Grapple, two crew members guarding the Pearl, ran to the deck after they saw Jack the Monkey fall, and went to see if there was an intruder. Elizabeth hid from the two pirates, and released the surviving crew of the Interceptor.

At the entrance to the cave, James Norrington and other Marines waited for the pirates to come outside, and ambush them. But that didn't go according the plan, and after a Royal Marine was killed on the Dauntless, he managed to ring the bell on the deck, signalling Norrington to return to the Dauntless to assist his men.

In the cave, Jack and Barbossa were duelling near the chest of Cortés. Barbossa threw his sword on the ground, claiming himself invincible, to then Jack stabbed Barbossa. Barbossa sighed, and pulled out Jack's sword, and stabbed Jack with it. Will looked over to think his friend was dying, but Jack stepped into the moonlight, and revealed he was cursed. He stole a piece of the cursed gold while no one was watching. Jack and Barbossa then continued their duel.

On the deck of the Black Pearl, the crew of the Interceptor used a suspended longboat of the Black Pearl to knock the guarding crew off. Elizabeth then ordered the crew to assist her in saving Will and Jack. The crew kept to the code, and sailed the Black Pearl off. Elizabeth took her longboat back to the island to save Will and Jack herself.

The crew aboard the Dauntless was close to giving up, but Norrington and his Marines arrived and helped to beat back the cursed Pirates.

In the cave, Jack and Barbossa were duelling a never ending duel, while Will did his best to defend himself from the cursed pirates. When Will lost his sword, he was about to be killed by Jacoby, but Elizabeth showed up, and used a long golden rod to smack Jacoby across the face, saving Will. The two then teamed up to kill the pirates using Jacoby's grenades that were planted inside of him before he reverted to his human form.

Lifting the Curse
"I feel...cold."

- Barbossa's last words before he dies from a gunshot.

Jack saw that the tide of the battle had turned, and he cut his hand with his wrist, placed his blood on the gold, and threw it off to Will, who was at the chest. Barbossa then pulled out his pistol, and aimed it at Elizabeth. Before Barbossa could fire, another shot went off, and Jack's pistol was smoking. Jack finally shot Barbossa after ten years. Barbossa claimed Jack wasted his shot, but Will then spoke, Barbossa turned around to see the last two pieces of gold fall into the chest, lifting the curse. Barbossa saw his bloody wound, and died.

Back on the Dauntless, the crew of the Black Pearl reverted to normal, and surrendered. Norrington claimed the Dauntless was the victor in battle.

Jack stole some of the gold from the cave, while Elizabeth and Will decided to return to the Dauntless so Elizabeth's fiancée, Norrington, would know she was safe. Jack then told Will that he should have told Elizabeth that he loved her there.

Jack ends up sharing a ride to the Dauntless with Will and Elizabeth. Jack had been told that the Black Pearl was gone, but Jack was proud of his crew for keeping to the code.

The Hanging of Jack Sparrow
Jack was sentenced to be hung at Port Royal, while Will was pardoned by Weatherby Swann. Elizabeth expressed her feelings on this harsh sentencing, but her father told her it was the law, and he and Norrington had to follow it.

Will then approached Elizabeth, and confessed his love for her. Will then ran off to throw a sword at the hangman's noose, leaving Jack to stand on it so he wouldn't be choked to death when the executioner pulled the lever. Will then began a duel with the executioner, and the two pirates ran off and did their best to avoid the Royal Marines.

They were eventually surrounded by Royal Marines, and Norrington, who held his sword to Will's neck. Elizabeth then stood between them, stating that she would die along with Will and Jack. Weatherby ordered the Marines to stand down, and Norrington let them go. Jack then stood at the end of Fort Charles, and claiming that they almost caught Captain Jack Sparrow, but then Jack fell into the ocean.

When it looked like Jack had nowhere to go, the Black Pearl sailed into Port Royal. Jack then swam over to his ship.

Norrington then stated he accepted Elizabeth's decision to stay with Will, and didn't bother to pursue Jack Sparrow. Gillette then asked what to do about Sparrow, but Norrington said Sparrow had a one day's head start. Weatherby then questions Elizabeth's decision after Norrington and the Marines left, and Elizabeth was sure she made the right decision. Will and Elizabeth shared their first kiss on the Caribbean sunset.

Jack got onto the Black Pearl, who was then greeted by Joshamee Gibbs. Jack questioned to them not keeping to the code, but Gibbs stated they were actual "guidelines". Anamaria then stepped aside from the Pearl's helm, and told Jack that he was free to Captain his ship. Jack took the helm lovingly, and ordered the crew to make sail. He then pulled out his compass, and began singing the pirate song Elizabeth taught him.

Source

 * Pirates of the Caribbean: The Curse of the Black Pearl