There are 12 Trophies that can be collected.

BRONZE

The Mailbox Ate My Mail!
[TJ&E] Defeat a Demon Mailbox

Fallen Angel
[TJ&E] Defeat a Cupid

Wh-wh-what Time Is It!?
[TJ&E] Wake up from a nap

This Earth Food Isn't Half Bad!
[TJ&E] Eat all of Earth's delicacies

It's All About The Kicks
[TJ&E] Dash with the Super Hitops

We're Unstoppable
[TJ&E] Fly across water using the Rocket Skates

Up, Up, And Away
[TJ&E] Fly using the Icarus Wings

Even Adults Like Presents
[TJ&E] Snag some goodies from Santa

Lovin' This Earth Lifestyle
[TJ&E] Jump in the bath on Floor 0

SILVER

Smell Ya Later, Earth!
[TJ&E] Clear the Fixed World

The Long Road To Funkiness
[TJ&E] Obtain a rank of FUNK LORD

GOLD

Word Up! Back To Outer Space!
[TJ&E] Clear a Random World

http://www.ps3trophies.com/forums/playstation-trophy-news/24788-toejam-earl-trophy-list.html