There are 11 Trophies that can be earned in this title.

Bronze

Meals Fit for a King… Queen… Whatever
Gave the MerLeader every kind of bait

She's Cute When She's Angry
Get Morgan angry by repeatedly checking out the mast

Fishing for Literalists
Caught a Red Herring

Talk to the Hook
Threatened a number of adversaries with a Hook

Nice Try
Heard the Secret of Donkey Island

Silver

Give Her a Hand
Kicked LeFlay off the Screaming Narwhal

Artifacts of LIfe
Get all of the Summoning Artifacts

Mighty Merperson Rescuer
Save the MerLeader from McGillicutty

Model of E-FISH-Ency
Read every fish joke

Ride 'Em, Pirate
Made LeChuck do something embarassing on the cliff

Gold

The BIG Finish
Sailed to the alleged resting place of La Esponja Grande

http://www.ps3trophies.org/game/tales-of-monkey-island-chapter-2/trophies/