There are 14 Trophies that can be earned in this title.

Bronze

Ready for the junkyard
Complete the first stage ('Zeus Sector') at any difficulty level

Piece of rock
Complete the third stage ('Ethia Ruins') at any difficulty level

System liberated
Complete the fifth stage ('Turady Deep Sea') at any difficulty level

Survivor
Clear challenge 'Survivor'

Collector
Clear challenge 'Collector'

Action Fan
Clear challenge 'Action Fan'

Chain Expert
Clear challenge 'Chain Expert'

Profiler
Clear challenge 'Profiler'

Rating Expert
Clear challenge 'Rating Expert'

Lucky Number 7
Collect an accumulated total of 77777 chain rings

Silver

Key Explorer
Collect all 35 secret keys

Gold

Challenge Master
Unlock and successfully pass 12 or more challenges

2 Secret

http://www.ps3trophies.org/game/soldner-x-2-final-prototype/trophies/