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

Bronze

The Unabridged Version
Listened to all of Max's audiobooks on vinyl in their entirety

For Insurance Purposes
Checked out every object in Max's inventory

Genius in its Simplicity
Heard all the details of Stinky's origin

All the Old Familiar Places
Collected all of Max's precious memory slides

Like Battery Acid and Pickle Juice
Heard at least five accounts of what nightmares taste like

Fire Retardant
Shot all of the Flaming Max spores

Quiet on the Set
Snuck into the frame of Satan's documentary at least twice

Silver

Maxtastic Voyage
Sent a rescue team into the body of Giant Max

Battery Park
Overcame the psychic powers to enter Max's brain

Just Ask For Directions Already
Found the location of the only thing that will save Max

Prepare for Surgery
Delivered the tool necessary to complete Max's brain surgery

Gold

The Happy Ending
Discovered a last-minute way to save Max

http://www.ps3trophies.org/game/sam-and-max-the-devils-playhouse-5/trophies/