There are 15 Trophies that can be collected.

Bronze

The High Cost of Repairs
Discover a way to fund repairs to the Game Machine.

We're Going to Put On a Show!
Get celebrity judges and security for the Battle of the Bands.

Strong Bad's Got Talent
Receive filled out entry forms for the Battle of the Bands.

It's A Sabotage!
Successfully sabotage all the other bands.

The Hidden Tracks
Find all 12 collectibles.

Truly, Truly Outrageous
Collect all costume items.

There is No Safe Word
Find all possible ways to abuse Strong Bad.

Homestar Runner: The Musical
Witness all musical moments from the case of Homestar Runner.

Expressions of Affection
Hear all the ways the residents of Free County, USA love what they love.

I Pilot the Limozeen Bus
Achieve a high score in 'Limozeen: Hot Babelian Odyssey'

Limozeen on My Shelf!
Collect all Limozeen Mini-Glasses.

ROCK ON!
Collect each band poster.

Manual of Style
Collect all pages to the 'Limozeen: Hot Babelian Odyssey' manual.

Silver

Impossibly Rocked Out
Achieve the highest possible Awesomeness level.

Gold

D.O.I. Rocks the House!
Perform the best rock show with D.O,I.

http://www.ps3trophies.org/game/strong-bad-cool-game-ep-3/trophies/