Bronze: 38
Silver: 10
Gold: 2
Platinum: 1
Total: 51 

Bronze

Discouraging Finish! (secret)
Use an Astral Finish with every character

Duh dun DUNNNN! (secret)
[STORY] Saw the True Ending

Animation Conservation (secret)
Used Rapid Cancel over 100 times

Stop Hitting Yourself (secret)
Used Counter Assault 30 times

Hands Where I Can See Them
[GALLERY] Collected over 50 illustrations

Spoonful of Sugar (secret)
Stayed afloat for over 25 seconds with Rachel

Carpal Tunnel
Exceed a total playtime of 25 hours

This Just Got Real (secret)
Caused a Double Down to occur

This is Important (secret)
Heard Noel say 'Hands off the panda!' over 100 times

Beautiful Arakune (secret)
Had a perfect match using Arakune

Legionnaire
Reached Lv. 10

You're the Best! Around!
[TRAINING] Dished out a total of over 1,000,000 damage

You Brute!
[Ranked Match] Three consecutive wins in Ranked Matches

Devil's Advocate (secret)
Used Ragna's 'Gauntlet Hades' over 100 times

Restraining Order (secret)
Used Barrier Burst over 30 times

I'm faster than anybody! (secret)
[Ranked/Player Match] Get First Strike five times in a row

Voyeur
[Player Match] Witnessed over 20 battles

Greased Pig (secret)
Successfully escaped 50 throws

I Am the Just Sword
[ARCADE/SCORE ATTACK] Defeated Hakumen

Irresistible (secret)
Hit the opponent with Tager\'s \'Spark Bolt\' more than six times in one round

Hat Trick (secret)
In one match, successfully pulled off 'Thirteen Orphans,' 'The Great Wheel,' and 'All Green'

Murakumo Activated
[ARCADE/SCORE ATTACK] Defeat v-13 in Arcade/Score Attack mode

I Can Reuild Her… (secret)
As Carl, decommission Nirvana three times in one round

Ride the Icening (secret)
Used Musou Senshouzan or Tosshougeki over 20 times in one round, and finished the opponent off

Ruler of Kagutsuchi
[Ranked Match/Player Match] Fought against all characters

In Living Color (secret)
Use all the color palettes of a single character

It's Go Time (secret)
Performed your first Astral Heat

I Like to Watch
[REPLAY THEATER] Collected five replays, other than your own

It's the Only Way to be Sure (secret)
Performed a 20 hit combo after the round is over

Cat-a-pult (secret)
Threw a Kaka kitten using Taokaka's Kitty Litter Special!

You Never Forget Your First (secret)
Performed your first Barrier Crush

That Was Incredible!
[Ranked Match] Won first victory in a Ranked Match

Be Gentle, It's My First Time
[Ranked Match] Played first Ranked Match

Wanderer
[Player Match] Played first Player Match

Hello World!
[STORY] Watched the opening

Designated Driver (secret)
Used Distortion Drive over 100 times

Bangarang! (secret)
Fought against Bang as Bang, and both activated the 'Fu-Rin-Ka-Zan

Their Numbers Count for Nothing (secret)
Performed an instant block 300 times

Silver

Dante
[ARCADE] Beat Arcade mode on HELL difficulty

Warrior
[Player Match] Fought a total of 150 battles

100 Trials
[Ranked Match] Fought over 100 battles

Praetorian Guardian
Reached Lv. 30 

Welcome to the Azure Nightmare (secret)
[ARCADE/SCORE ATTACK] Defeat 'Unlimited' Ragna, and obtain the power

It's over 10,000! (secret)
Dealt over 10,000 damage using Hakumen, without the use of an Astral Heat

Nothing's Gonna Keep You Down (secret)
Earned a Perfect victory 30 times

Activate Termination Protocol (secret)
Completed a 60+ hit combo using Nu.

Victory is an Illusion (secret)
[ARCADE/SCORE ATTACK] Defeat 'Unlimited' Rachel

Words Hurt Too (secret)
Let your opponent get a 5,000 hit-point lead on you, then taunt you

Gold

Leonidas
[SCORE ATTACK] Beat Score Attack mode

200 Trials
[Ranked Match] Fought over 200 battles

Platinum

Platinum
Unlock all other trophies

Source: This list was compiled using two incomplete sources: http://playstation.joystiq.com/2009/07/10/trophies-blazblue/ & http://www.psu.com/ps3-trophies/blazblue_calamity_trigger/