There are 12 Trophies that can be collected.

BRONZE

Punitive Soldier
You've put down a power holder.

Story1 Completed
You've completed the story mode"Subjugation".

Story2 Completed
You've completed the story mode"REBIRTH".

No Guard
You've gone cleared a scene without any guard.

Counter Master
You've succeded in all of the counter actions.

Debut in Our Ranking
You've made a debut in our ranking.

100 Chained
You've achieved a chain of 100.

SILVER

No Restart
You've completed the two story mode on Normal difficulty without using a continue feature.

1 Kill Cleared
You've gone cleared this scene by defeating exclusively the scene boss.

No Malice
You've gone story mode "REBIRTH" was completed without using the power hidden in the Spirit Vessel.

All S Rank
You've gone clear all scenes on Normal difficulty at S rank.

GOLD

No Repair
You've completed the two story mode on Normal difficulty without repairing the Spirit Vessel or using a continue.

http://www.ps3trophies.org/game/malicious-rebirth-vita/trophies/