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

Bronze

The Violet Beauregard Memorial Trophy
Tried every piece of gum

Say What?
Discovered Morgan's Dying Words

Grog, Grog, Grog!
Used a dollar bill to try to buy every drink in the Grog Machine

Dance, Monkey, Dance!
Did the dance of the hybrid fruit

Grave Ribber
Read every gravestone

Silver

All Roads Lead to LeChuck
Opened the Crossroads

I Ain't Got No Body
Bound Guybrush's spirit to his body

Does This Corpse Make Me Look Fat?
Completed the Diet of the Senses

A Credit to Pirates Everywhere
Witnessed Morgan's Final Fate

Morgan's Secret
Found out what Morgan treasures above all else

Gold

Fall of the Pirate God
Defeated LeChuck

http://www.ps3trophies.org/game/tales-of-monkey-island-chapter-5/trophies/