There are 53 Trophies that can be collected.

Bronze

Welcome to [orgarhythm]
Began playing [orgarhythm]

First Tutorial
Cleared tutorial for the first time

Diligence
Cleared all tutorials

[Dark Beats] cleared!
Cleared [Dark Beats]

[Flying Cannon] cleared!
Cleared [Flying Cannon]

[Surface of the Wasteland] cleared!
Cleared [Surface of the Wasteland]

[Squall] cleared!
Cleared [Squall]

[Holy Oratorio] cleared!
Cleared [Holy Oratorio]

[Nameless Goddess] cleared!
Cleared [Nameless Goddess]

[Second Beat] cleared!
Cleared [Second Beat]

[Cannon of Revenge] cleared!
Cleared [Cannon of Revenge]

[Dark Ballroom] cleared!
Cleared [Dark Ballroom]

[Soaring Demons] cleared!
Cleared [Soaring Demons]

[Inspiration and Exploration]
Cleared [Inspiration and Exploration]

[Bloody Battle]
Cleared [Bloody Battle]

[Normal] difficulty level cleared!
Cleared all in [Normal] difficulty

Zero Deaths
Cleared a map without losing a single warrior

God Bless
Used a support skill

Trails in the Heavens
Drew a line through [Dragging]

Voltage Up
Increased voltage rank

MAX Voltage
Raised voltage rank to max level

Carnivorous
Invoked [Attack] support skill 100 times

God of Healing
Invoked [Heal] support skill 100 times

Conservative
Invoked [Guard] support skill 100 times

Stopper
Invoked [Slow] support skill 100 times

Marathon Runner
God of Light movement distance passed 42.195km

Suite 10
10 clears achieved

Groove
50 clears achieved

S-Hunter
Achieved S-Rank 5 times

Battlefield Musician
Achieved S-Rank 10 times

Standing Alone
Cleared a map without using any support

Striker
Deployed 1,000 [Strike] troops

Master of Archery
Deployed 1,000 [Archer] troops

Hail of Stones
Deployed 1,000 [Catapult] troops

Face of the Devil
Deployed 1,000 [Sacrifice] troops

Dark Hunter
Defeated 10,000 Dark Tribe warriors

Finding Friendly Faces
Played in co-op mode

Comrade-in-Arms
Cleared a map in co-op mode

Discord
Acquired Game Over in co-op mode

Rival
Played in versus mode

Winner
Won in versus mode

Loser
Lost in versus mode

Sound Director
Altered the sound volume in-game

Cinema Enthusiast
Played all movies

Spirited Away
Failed to inflict any damage to enemy with [Sacrifice] skill

Silver

[Hard] difficulty level cleared!
Cleared all in [Hard] difficulty

Conductor of Many Orders
[Dragging] length exceeded 100 miles

Eccentric
100 clears achieved

Carnival Soldier
Achieved S-Rank 20 times

Universal
Acquired all skills (excepting for DLC)

Gold

Orgarhythmer
Achieved S-Rank in all stages and on all difficulty levels

No Sense of Rhythm
Achieved 100 bad taps in a row

Platinum

All Clear
Obtained All Other [orgarhythm] trophies

http://www.ps3trophies.com/forums/playstation-trophy-news/19502-orgarhythm-trophy-list.html