There are 15 Trophies that can be collected.

Bronze

A Dame in Shoes
Get hired by renowned Rainforest conservationalist Sweetsey Buttons.

Recover the Serum
Obtain the serum to save the Rainforest.

The Man with the Plan
Obtain the plans and access to Uzi Bazooka's Hideout.

Requisitionist for Hire
Recover the Rocket Parts for the scientist.

No Stone Unturned
Find all 12 collectibles.

Look the Part
Find all costume pieces.

I Reach for My Nunchuk…
Nunchuk all possible characters.

I Know People
Give not-so-subtle hints to who you know (of).

Continuity Errors
Find all bad takes in 'Dangeresque 3: The Criminal Projective'.

Space Circus Ringleader
Obtain a high score of 900 points in 'Space Circus Catastrophe!'.

How to Join the Circus
Collect all pages to the 'Space Circus Catastrophe!' manual.

Merchandising! Merchandising! Merchandising!
Obtain all pieces of Dangeresque 3 Merchandise.

I Got a Bullet With Your Name On It
Obtain all bullets with names on them.

Silver

Codename: Awesome!
Achieve the highest possible Awesomeness level.

Gold

Stick it to the Man!
Find out who the real villain is and stop him!

http://www.ps3trophies.org/game/strong-bad-cool-game-ep-4/trophies/