Here is the full list of all 41 LEGO Pirates of the Caribbean trophies - there are 25 bronze, 12 silver, 3 gold and 1 platinum.
Unlock all the Jack Sparrow characters (Single Player Only)
Fire 100 cannonballs
Defeat 100 enemies
Do 5 lady backflips in a row
Complete the Film 1 story
Use a spyglass
Watch a sunset
Complete Port Royal in Story with zero studs
Get eaten by a creature in deadly water
Test any custom character
Play a level in co-op
Complete Port Royal in Story without dying
Complete Port Royal
Collect all Trophies.
Complete the Film 2 story
Complete the Film 3 story
Complete the Film 4 story
Collect all Gold bricks (Single Player Only)
Complete the game to 100% (Single Player Only)
Unlock all the cursed Black Pearl crew characters (Single Player Only)
Unlock all the Flying Dutchman crew characters (Single Player Only)
Unlock all the Queen Anne's Revenge crew characters (Single Player Only)
Collect all the red hats (Single Player Only)
Unlock all Elizabeth characters (Single Player Only)
Unlock all the Pirate Lord characters (Single Player Only)
Complete the Brethren Court
Complete all the Guard Dog levels
In any level use only the compass to find all it's secrets in one go, alone.
Sail all the minikits in the hub
Unlock all characters (Single Player Only)
Play as all the Extra Toggle characters
Hit a flying parrot on Smuggler's Den
Reach 888,888,888 studs
High dive into the Maelstrom
Get True Pirate in all levels (Single Player Only)
Ride on all types of animal in the game
Walk on the sea bed with all possible characters
Play a level with all Extras turned on (Single Player Only)
As Jimmy Legs, whip Will Turner 5 times
Highlight the secret 6th point on all 4 level select maps (Single Player Only)
Get eaten by the Kraken 10 times