There are 20 Trophies that can be collected.

Bronze

Starboretum    
Complete the main game.

Safety    
Complete "200" without any of your own trees being destroyed.     

Lightyear    
Complete "The Centre Cannot Hold" within 60 minutes.     

Lightsecond    
Complete the campaign in under ten hours.     

Pacifism    
Complete "Protection" without destroying anyone else's trees.     

Martyrdom    
Attack an enemy asteroid and lose 300 seedlings in the process.     

Hero    
Find over 600 of the lost seedlings in the game.     

Aggressor    
Attack an enemy asteroid and destroy 200 seedlings in the process.     

Traveller    
Discover an asteroid using a flower or a mine.     

Panspermia    
Send a flower or a mine over 50000 arbitrary distance units.     

Gardener    
Gather ten flowers on an asteroid.     

Minefield    
Gather five mines on an asteroid.     

Attrition    
Battle for an enemy asteroid for ten minutes.     

Besieged    
Defend one of your own asteroids continuously for five minutes.     

Stalemate    
A pitched battle that lasts over 15 minutes and incurs 500 losses between all sides.     

Banzai    
Destroy ten enemy seedlings using a mine explosion.     

Intruder    
Land a beacon seed on an enemy asteroid.     

Historian    
Record all of the Ancient Artifacts.     

Uplift    
Terraform an asteroid to maximum attributes.

Silver

Illuminator    
Complete Dark Matter Mode.

http://www.ps3trophies.org/game/eufloria/trophies/