There are 14 Trophies that can be collected.

Bronze

Amuse Bouche
Eat the final cork in Level 1

Graduation Dinner
Eat the valedictorian at the end of Chapter 1

Houston, we have a problem
Board the rocket ship at the end of Chapter 2

It Came From Outer Space
Take a ride on the space elevator at the end of Chapter 3

Getting the Boot
Boot yourself over the spikes at the end of Chapter 4

Delicious Magnetic Balls!
Eat the magnetic balls at the end of Chapter 5

Not too shabby
Earn a silver medallion or better in five levels

Jealous?
Look up the top score on any leaderboard

Finally, monsieur, a wafer thin mint
Absorb 1500 objects

Extinction
Eat all of the escape pods in the final level

Master Tilter
Complete all of the Tilt-A-Blob levels

Silver

Blob Friends Forever
Collect all Blob Friends in the game

Gold

Golden Blob
Earn a gold medallion in every level

1 Secret

http://www.ps3trophies.com/forums/playstation-trophy-news/12035-tales-space-mutant-blobs-attack-trophy-list.html