There are 51 Trophies that can be earned in this title.

Bronze

Well, It's Something to Do…
[Arcade / Score Attack] Hold your own against Unlimited Hazama.

Tall, Dark, and Handsome
[Arcade / Score Attack] Put Unlimited Ragna in his place.

Blood on Your Hands
[Score Attack] Defeat Unlimited Rachel.

Level One…!
[Story] Watch 'Previously on…' and 'Opening' in Story Mode.

That's the End of That Chapter
[Story] View any character's canon ending in Story Mode.

Ragna Cum Laude
[Tutorial] Finish all your homework.

Napoleon Bonaparte
[Legion] Conquer the map on 'Easy.'

Alexander the Great
[Legion] Conquer the map on 'Normal.'

I'm on Top of the World!
[Player Match] Earn your first victory.

I Can Quit Any Time I Want!
[Player Match] Win more than 100 matches.

Aniki Is Watching You
[Player Match] Observe more than 10 matches.

Two Men Enter. One Man Leaves.
[Ranked Match] Earn your first victory.

I Get Around
Use every single character.

They Call Me MISTER Tiddles!
Use an Astral heat for the very first time.

Real Ultimate Power
Used every character's Astral Heat.

It'll Only Hurt for a Minute
Your first Guard Crush.

Don't Touch the Merchandise
Instant Block more than 20 times in one round.

Hold On Loosely
Cause more than 30 Throw Reject Misses.

M.C. Hammer
Escape more than 5 throws in one round.

You Broke My Heart!
Finish an opponent immediately after a normal Break Burst.

Fatality
Land more than 30 Fatal Counters.

The Better Part of Valor
Do not take damage for 20 seconds while in Negative State, and win the round.

Well, It's Not!
Using Ragna, land 'Not Over Yet' more than three times during a match.

Ice-Ten
Using Jin, freeze your opponent more than 10 times during a match.

Are You There God? It's Me, Noel
Using Noel, hit the opponent with her 'Silencer' more than 10 times during a match.

Twirling toward Freedom
Using Rachel, land a '6C' attack more than 30 times during a match.

1.21 Gigawatts!
Using Tager, land 'Spark Bolt' more than five times during a match.

Taut Taunts
Using Taokaka, land 5 taunts over the course of a match.

Four Sheets to the Wind
Using Litchi, land 'Four Winds' more than 4 times during the course of a match.

BEES!
Using Arakune, unleash a 70-hit combo.

Loincloth Festival
Using Bang, land a total of 3 Astral Heats.

The Clap
Using Carl, keep an opponent airborne for more than 7 seconds.

You're Already Dead
Using Hakumen, dish out over 10,000 damage in one combo.

Lamb to the Slaughter
Using Lambda, land a 50-hit combo.

For Great Justice
Using Tsubaki, use the 'D' version of every single special attack in a combo.

Beachball!
Using Hazama, keep an opponent airborne for more than 7 seconds.

Murakumo, AWAKEN!
Select Mu.

Silver

Superior State of Mind
[Challenge] Beat more than 100 challenges.

Genghis Khan
[Legion] Conquer the map on 'Hard.'

Only the Hard, Only the Strong
[Ranked Match] Fight more than 100 battles.

Gold

Mint Condition
[Gallery] Collect all of the…collectibles.

Secret Trophies

Bronze

Is…Is That All?
[Story] Unlocked the True Ending in Story mode.

I Can Do This All Night
[Training] Practiced for over one hour straight.

There Can Be Only One
[Network] Fought against every character.

Rear Window
[Replay Theater] Watched replays of more than 20 different matches.

Ding!
[Network] Reached D-code level 25.

Silver

Hell Yes
[Arcade] Completed Arcade Mode on

Ding Ding!
[Network] Reached D-code level 50.

Gold

Score!
[Score Attack] Beat Score Attack mode.

All Good Things
[Story] Finished the True Ending in Story mode.

Platinum

Hidden Trophy

http://www.ps3trophies.org/game/blazblue-continuum-shift/trophies/