There are 12 Trophies that can be earned in this title.

Bronze

Speed Demon
Complete the game in under three hours

Free Thinker
Beat the game using fewer than 10 hints

Old School
Switch to classic mode at least once

Five Minutes Later…
Allow Guybrush to die.

Turning the Lights Out
Complete the game using object highlighting five times or less.

Helium Inhaler
Make Guybrush inhale some helium

Call 911
Call the LucasArts helpdesk when walking through the jungle on Dinky Island

Silver

Complete part one
Complete part one: The Largo Embargo

Complete part two
Complete part two: Four Map Pieces

Complete part three
Complete part three: LeChuck's Fortress

Monkey Master
Beat the game without using a hint

Gold

Complete part four
Complete part four: Dinky Island

http://www.ps3trophies.org/game/monkey-island-2-le-chucks-revenge/trophies/