There are 33 Trophies that can be collected.

BRONZE

Bachelor of Escapology
Escaped from the elevator.

Master of Escapology
Escaped from eight rooms.

Escapey
Escaped on Hard difficulty.

Classified
Found a secret.

An Eidetic Experience
Found a file.

Every Ending Begins Somewhere
Saw any of the endings.

That Wasn't Supposed to Happen
Saw any of the bad endings.

SILVER

Doctor of Escapology
Escaped from sixteen rooms.

GOLD

A Consummate Collection
Found ALL the files!

PLATINUM

Virtue's Last Reward
Acquired all trophies.

23 SECRET

BRONZE

To Each According to His Needle
Opened the first lock.

I Can't Believe It's Not Murder!
Opened the second lock.

Gotta Hand It To You
Opened the third lock.

If I Told You You Had A Nice Antibody…
Opened the fourth lock.

He Was Convicted of a String of Numbers
Opened the fifth lock.

No Lying Down On the Job
Opened the sixth lock.

Who Set Up Us The Bomb, Part 1
Opened the seventh lock.

Why'd You Do That, You Dumas!
Opened the eighth lock.

Who Set Up Us The Bomb, Part A
Opened the ninth lock.

Some Days You Just Can't Get Rid of a Bomb
Opened the tenth lock.

SILVER

Tears in the Rain
Saw Luna's ending.

Through the Looking Glass
Saw K's ending.

Behind Blue Eyes
Saw Dio's ending.

In Root Beer Veritas
Saw Tenmyouji's ending.

An Equal and Opposite Reaction
Saw Quark's ending.

Secret Agent Woman
Saw Clover's ending.

Best Served Cold
Saw Alice's ending.

Arms Race
Saw Sigma's ending.

Time After Time
Saw Phi's ending.

GOLD

Escapest
Escaped everything on Hard difficulty.

Redacted
Found ALL the secrets!

Fire and Ice
Saw the end. Or maybe the beginning?

A Certain Point of View
Caught a glimpse of another time.

http://www.ps3trophies.org/game/zero-escape-virtues-last-reward/trophies/