Barbossa - Complete Shipreck City in Story mode.

Characters - Complete the indicated task to unlock the corresponding character.

Ammand The Corsair: Complete the Pirate Poker sub-mission on the Shipwreck City level
.
Black Bart: Complete the Combat Challenge on the Maelstrom level.
Bootstrap Bill Turner: Complete the Defeat Enemies sub-mission on the Prison Fortress level.

Cannon Arm: Complete the Combat Challenge on the Pearl vs. Kraken level.
Capitain Chevalle: Complete the Port Royal level.
Captain Barbossa: Complete the Shipwreck City level.
Captain Elizabeth Swann: Complete the Combo Challenge on the Davy Jones Locker level.
Captain Jack Sparrow: Complete the Prison Fortress level.
Captain Sao Feng: Complete the Singapore level.
Captain Teauge: Complete the Combat Challenge on the Prison Fortress level.
Cotton: Complete the Rescue sub-mission on the Isla de Pelegostos level.

Davy Jones: Complete Pearl vs. Dutchman level.

Elizabeth Swann: Complete the Tortuga level.

Gentlemen Jocard: Complete the Davy Jones Locker level.
Gibbs: Complete the Combat Challenge on the Port Royal level.
Governor Swann: Complete the Combat Challenge on the Pearl vs. Dutchman level.

James Norrington: Complete the Combat Challenge on the Tortuga level.

Lian: Complete the Combat Challenge on the Singapore level.
Lord Cuttler Beckett: Complete the Maelstrom level.

Mercer: Complete the Hit-Combo sub-mission on the Singapore level.
Mistress Ching: Complete the Jackanism on the Tortuga level.
Mordillah: Complete the Combo Challenge on the Prison Fortress level.

Pintel: Complete the Isla Cruces level.

Ragetti: Complete the Combat Challenge on the Isla Cruces level.

Sri Sumba Jee: Complete the Combat Challenge on the Shipwreck City level.

Tai Huang: Complete the Sea Battle level.
Tia Dalma: Complete the Missing Person sub-mission on the Port Royal level.

Villanueva: Complete the Combo Challenge on the Tortuga level.

Will Turner: Complete the Isla de Pelegostos level.

Isla Cruces Level: Gold Idol Location - When you get to the waterfall where enemies attack you, defeat them all. Then, walk into the waterfall. Behind the waterfall is a secret room with the gold idol.

Shipwreck City: Gold Bars - This is the only level where you must go over an area twice to find the items. After you receive the captain's Piece Of 8 from the thief, you must go back over the area you traveled along to get to the thief (i.e. cut loose the rafts again and jump across). The second time you travel along this path, the gold bars will appear.

The following swords are listed by order of strength. Complete the indicated task to unlock the corresponding sword.

Cutlass: Default sword
Dutchman sword: Complete the Pearl Vs Dutchman level.
Norrington sword: Complete the Isla Cruces level.
Bone sword: Complete the Davy Jones' Locker level.
Gun sword: Complete the Sea Battle level.
Pirate King's sword: Complete the Shipwreck City level.
Davy Jones' sword: Complete the Maelstrom level.
Ghost sword: Complete the Hit Combo sub-mission on the Isla Cruces level.
Legend sword: Complete the Hit Combo sub-mission on the Maelstrom level.

Complete the following achievements to unlock Xbox Live Gamerscore points.

Eleven Calypso Pieces (150 points): Find the hidden Calypso piece on each level to unlock the story of Davy Jones and Calypso.
Seven Letters (25 points): Collect all seven Letters, lost throughout the Prison Fortress.
Seven Periwigs (25 points): Collect the seven Periwigs hidden around Port Royal.
Seven Nautilus Shells (25 points): Collect the seven Nautilus shells, scattered throughout the Flying Dutchman.
Seven Pirate Flags (25 points): Collect the seven Pirate Flags of Tortuga, hidden in chests and secret areas.
Seven Paprika Tins (25 points): Collect the seven Paprika tins of Isla Cruces.
Seven Bottles of Rum (25 points): Collect the seven bottles of Rum (hidden in the Black Pearl) during the Kraken's attack.
Seven Sea Charts (25 points): Collect the seven Sea Charts from the streets of Singapore.
Seven Skulls (25 points): Collect the seven Skulls hidden throughout Davy Jones' Locker.
Seven Tarot Cards (25 points): Collect the seven Tarot cards lost around the Flying Dutchman.
Seven Gold Bars (25 points): Gold - every pirate's dream! Collect the seven gold bars of Shipwreck City.
Seven Pirate's Dice (25 points): Collect the seven Pirate's dice, lost around the Flying Dutchman and the Black Pearl.
Prison Fortress Treasure (25 points): Open the Jackanism chest in the Prison Fortress, and unlock bonus material in the Treasure Trove.
Port Royal Treasure (25 points): Open the Jackanism chest in Port Royal, and unlock bonus material in the Treasure Trove.
Tortuga Treasure (25 points): Open the Jackanism chest of Tortuga, and unlock bonus material in the Treasure Trove.
Isla Cruces Treasure (25 points): Open the Jackanism chest in Isla Cruces, and unlock bonus material in the Treasure Trove.
The Kraken Treasure (25 points): Open the Jackanism chest in the Black Pearl, and unlock bonus material in the Treasure Trove.
Davy Jones' Locker Treasure (25 points): Open the Jackanism chest of Davy Jones' Locker, and unlock bonus material in the Treasure Trove.
Shipwreck City Treasure (25 points): Open the Jackanism chest in Shipwreck City, and unlock bonus material in the Treasure Trove.
The Maelstrom Treasure (25 points): Open the Jackanism chest of the Maelstrom, and unlock bonus material in the Treasure Trove.
Jack's second finish move (25 points): Unlock Jack's second finish move by escaping from the Prison Fortress.
Jack's third finish move (25 points): Unlock Jack's third finish move by surviving the Kraken's attack.
Jack's fourth finish move (25 points): Unlock Jack's fourth finish move by escaping from Davy Jones' Locker.
Will's second finish move (25 points): Unlock Will's second finish move by saving Chevalle and leaving Port Royal.
Will's third finish move (25 points): Unlock Will's third finish move by stealing the key from the Flying Dutchman.
Will's fourth finish move (25 points): Unlock Will's fourth finish move by surviving Isla Cruces.
Elizabeth's second finish move (25 points): Unlock Elizabeth's second finish move by locating Mistress Ching and Villanueva in Tortuga.
Elizabeth's third finish move (25 points): Unlock Elizabeth's third finish move by surviving Isla Cruces.
Elizabeth's fourth finish move (25 points): Unlock Elizabeth's fourth finish move by exploring and escaping from Singapore.
Collect 100 Souls (150 points): Collect one hundred souls from your enemies using the power of the Jackanism sword.