The game has 13 trophies

Bronze

Is This Your Card?
Read the mind of everyone aboard General Skun-ka'pe's flagship.

Soothsayer
Saw a future vision for Sam in every possible environment.

To the Five Boroughs
Visited every location available in this case.

Crime-Tron
Used all of the correct combinations of clues in the Crime-Tron.

Pret-a-teleporter
Teleported to every available phone in the case.

Ask Your Parents
Heard 7 references no one under the age of 30 will understand.

Don't Ask Your Parents
Heard 10 double entendres.

Frequent Flier
Smacked Max out of the way in every environment.

Part of a Nutritious Breakfast
Used the Nutrition Specs to reveal a secret object.

Silver

We're on the Case!
Sent General Skun-ka'pe to the Penal Zone in Max's future vision.

The Brain Awakens
Brought the Alien Brain back to life.

Ape Escape
Tracked down General Skun-ka'pe.

Gold

The Penal Zone
Sent General Skun-ka'pe to the Penal Zone once and for all.

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