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

Bronze

What's in a Name?
Found out the horrifying truth about Bosun Krebbs

What Do You Do with a Drunken Guybrush?
Drank everything available in Club 41

Musical Memories
Enticed Guybrush to indulge his musical impulses

Push ze Buttons of SCIENCE!
Tried all four of buttons in De Singe's Lab

Idiot for a Client
Explored the possibilities of Guybrush calling himself to the stand

Silver

Ayyyye, the Jury
Got Civil charges against Guybrush dropped

Use the Source
Got criminal charges dropped… with a little help

Feast for the Senses
Almost completed the Feast of the Senses

Shlock Shopper Supreme
Fully Perused Stan's Wares

Guybrush Goes Classy
Experienced Guybrush's Brush with the Bard

Gold

Adieu, Adieu..
Defeated De Singe

http://www.ps3trophies.org/game/tales-of-monkey-island-chapter-4/trophies/