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