There are 37 Trophies that can be earned in this title.

Bronze

Everyone's Hero
Defeat more than 100 monsters.

Planetary Hero
Defeat more than 300 monsters.

Galaxy Hero
Defeat more than 800 monsters.

Seeker of Victory
Win in battle 30 times.

Seeker of More Victory
Win in battle 100 times.

Seeker of Annihilation
Win in battle 300 times.

Power of the Earth
Total Damage in a Fury Chain exceeds 10,000.

Power of the Sun
Total Damage in a Fury Chain exceeds 50,000.

Power of the Cosmos
Total Damage in a Fury Chain exceeds 100,000.

Be the Space Debris
Hit Count in a Fury Chain exceeds 300.

Be the Comet
Hit Count in a Fury Chain exceeds 500.

Be the Shooting Star
Hit Count in a Fury Chain exceeds 700.

Art Appreciation
Obtain 10 Managraphic Images.

Treasure Hunter
Discover 30 concealed treasures.

The Space Cleaner
Drift 10 dungeons out of orbit.

The Bourgeois
Spend 100,000G at the Shop.

Managraphic Addict
Spend 1,000,000G at the Managraphic Workshop.

Galaxy Miser
Hold over 1,000,000G.

Meteorite Star
Create 100 Meteorites.

Material Star
Synthesize 100 items.

Monster Star
Create 100 Monsters.

Space Tourists
Let yourself drift out of orbit 50 times.

Silver

Game Maniac
Get over 1,000,000 Evaluation Points.

Shopaholic
Spend 1,000,000G at the Shop.

Closet Otaku
Obtain 30 Managraphic Images.

Museum Creator
Discover 60 concealed treasures.

Be the Meteor Shower
Hit Count in a Fury Chain exceeds 1,000.

Power of Creation
Total Damage in a Fury Chain exceeds 300,000.

Seek Obliteration
Win in battle 500 times.

The Space Scrubber
Drift 50 dungeons out of orbit.

Deep Space Hero
Defeat more than 1,300 monsters.

Gold

Hero of the Universe
Defeat more than 2,000 monsters.

What is truth, dood?
Complete the true ending route.

Space Activists
Drift 100 dungeons out of orbit.

The Debtor
Spend 3,000,000G at the Shop.

The Strongest Harem
Every character's Level is 100 or higher.

Platinum

The Platinum Prinny
All that work for this, dood?

http://www.ps3trophies.org/game/trinity-universe-us/trophies/