Successfully complete one of the following tasks to get a trophy:

Amuse Bouche (Bronze): Eat the final cork in Level 1.
Graduation Dinner (Bronze): Eat the valedictorian at the end of Chapter 1.
Houston, we have a problem (Bronze): Board the rocket ship at the end of Chapter 2.
It Came From Outer Space (Bronze): Take a ride on the space elevator at the end of Chapter 3.
Getting the Boot (Bronze): Boot yourself over the spikes at the end of Chapter 4.
Delicious Magnetic Balls! (Bronze): Eat the magnetic balls at the end of Chapter 5.
Not too shabby (Bronze): Earn a silver medallion or better in five levels.
Jealous? (Bronze): Look up the top score on any leaderboard.
Finally, monsieur, a wafer thin mint (Bronze): Absorb 1500 objects.
Extinction (Bronze): Eat all of the escape pods in the final level.
Master Tilter (Bronze): Complete all of the Tilt-A-Blob levels.
Blob Friends Forever (Silver): Collect all Blob Friends in the game.
Golden Blob (Gold): Earn a gold medallion in every level.

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Golden Blob Trophy in Tales from Space: Mutant Blobs Attack: Earn a gold medallion in every level - worth 90 Trophy XP. Find guides to this trophy here. The best place to get cheats, codes, cheat codes, walkthrough, guide, FAQ, unlockables, tricks, and secrets for Tales From Space: Mutant Blobs Attack for PC. Pathetic humans, beware! Sign up here for updates: press kit.

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Additionally, there is one secret trophy:

Galaxicide (Bronze): Eat the solar system.