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

Bronze

Leave Well Enough Alone
Experienced a brief, yet horrifying transformation

Why is My Older Brother Laughing?
Encountered a shipload of references to the previous Monkey Island games

The Sounds of Science
Heard DeSinge treating four different patients

Bats Right, Throws Lame
Repeatedly Threw Things… Kinda

Is That a Pox On Your Face, Or Are You Just Angry To See Me?
Experience the effects of the Pox on the charming inhabitants of Flotsam

Silver

The Legend of LeFlay
Quizzed everyone about Morgan LeFlay

This Ain't a Library
Intensely browsed a prominent bookshelf

LeChuck Slayer
Defeated LeChuck (again)

Use the Source
Met Deep Gut

The Winds of Freedom Blow
Escaped from Flotsam Island

Gold

Many Unhappy Returns
Found Elaine

http://www.ps3trophies.org/game/tales-of-monkey-island-chapter-1/trophies/