There are 50 Trophies that can be collected.

Bronze

Battle of the 12 Gold Palaces
Complete Palace of Aries in the story mode

Aldebaran, the Golden Bull
Complete Palace of Taurus in the story mode

Between Life and Death
Complete Palace of Cancer in the story mode

Awaken, Aiolia!
Complete Palace of Leo in the story mode

The Phoenix Rises Again
Complete Palace of Virgo in the story mode

The Sword of Libra
Complete Palace of Libra in the story mode

The Last Scarlet Needle
Complete Palace of Scorpio in the story mode

Athena Is Yours
Complete Palace of Sagittarius in the story mode

The Forbidden Strike
Complete Palace of Capricorn in the story mode

Quest for Absolute Zero
Complete Palace of Aquarius in the story mode

Nebula Stream Explodes!
Complete Palace of Pisces in the story mode

Saori Rescued
Save Athena in the story mode (any difficulty)

Thirteen Years Ago…
Finish the Aiolos chapter in the story mode (any difficulty)

End of a Legend
Finish all stories and stages in story mode (any difficulty)

Saint of Hope
Finish the Sanctuary arc of story mode in Normal mode (cannot change difficulties midway)

The Legend Reborn    
Finish the Sanctuary arc of story mode without using a continue (any difficulty)

All I can Rely On…Is My Power    
Win a boss battle without using a continue (any opponent)

Senseless Mastery    
Win a boss battle without using any 7-Sense (any opponent)     

Start of the Battle    
Finish 1 Single Challenge course in mission mode     

End of the Struggle    
Finish 10 Single Challenge courses in mission mode

We Will Die Together, My Brother    
Finish 1 Tag Challenge course in mission mode     

I Don't Need My Cloth!    
Finish a course in mission mode with a character who's taken off his Cloth     

We're All In This Together    
Unlock all characters in the mission mode character select screen

The Unwavering Warrior    
Earn A rankings in 10 stages or courses

Cosmo Skills Unleashed    
Use all Burst attacks while in Cosmo Burst mode     

Big Bang Unleashed    
Use a Big Bang Attack for the first time     

Awakening    
Pull off a Real 7-Sense move 7 times     

I'll Remove It Now!    
Remove your Cloth as Shiryu     

I Knew You'd Come For Me!    
Have Ikki appear when continuing as Shun     

A True Phoenix    
Remove your Cloth as Ikki     

A 1000-Day War    
Use a Gold Saint to defeat another Gold Saint     

Pulverizing to Atoms    
Destroy 100 breakable objects

Rend the Skies, Destroy the Earth    
Use Cosmo Points to raise your abilities

To the Galaxies    
Upload mission mode data to the online ranking     

Blood-Stopping Master    
Use Shinoten to save friends 10 times in Tag Challenge courses

Silver

Saint of Speed    
Finish the Sanctuary arc of story mode in Hard mode (cannot change difficulties midway)

Worthy of the Pope    
Win 100 battles against Gold Saints

The True Victor    
Win a boss battle without taking damage (any opponent)

Beyond the Fight    
Finish all Single Challenge courses in mission mode

The Same Attack Never Works Twice    
Use all Big Bang Attacks from all characters

Dodge the Needles    
Defeat Scorpio Milo without getting hit by Scarlet Needle

Gold

String of Miracles    
Earn A rankings in all stages and courses

Axia Complete    
Complete your gallery collection

Platinum

Eternal Legend    
Collect all Trophies

4 Secret

Bronze

Shina's All Yours    
Defeat Cassios     

Praise My Beauty…    
Defeat Misty     

Black Saint Extermination    
Defeat all the Black Saints

Gold

Saint of the Goddess    
Finish the Sanctuary arc of story mode in Bronze mode (cannot change difficulties midway)

http://www.ps3trophies.org/game/saint-seiya-sanctuary-battle/trophies/