There are 13 Trophies that can be collected.

Bronze

Acid Test
Test your strength by flying through a running stream of acid.

Just Add Water
Douse cellular fluid with water.

Drop It Like It's Hot
Use a rock to defeat an enemy with the Hungry Suit.

Thread the Needle
Defeat a Bullet Stormster.

Ghost Buster
Dispel 5 or more Phantoms in one area with the Light Suit.

Use the Centripetal Force!
Defeat an enemy using teh Super Spin,

One Small Step
Purchase an item in Online Battle.

You've Got to Know When to Hold 'em
Win an online battle you have bet on.

One Giant Leap
Advance to a higher league through Online Battle.

Silver

A Glint In Your Eye
Get all the treasure from Episode 4 – not including a Perfect Rescue Bonus.

A Girl's Best Friend
Get all the treasure from Episode 5 – not including a Perfect Rescue Bonus.

Diamond Finger
Get all the treasure from Episode 6 – not including a Perfect Rescue Bonus.

Gold

Exodus Hominis
Safely rescue all survivors – including the special survivors.

http://www.ps3trophies.org/game/pixeljunk-shooter-2/trophies/