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

Bronze

Start with the Corners
Found your first puzzle piece

Puzzle of Flesh
Found 1/4 of the puzzle pieces

Starting to come together
Found 1/2 of the puzzle pieces

Paper-Mache
Found your first Billy Puppet

A Little Background
Found your first Case file

Some light reading
Found 1/4 of the Case Files

Half the story
Found 1/2 of the Case Files

Play ME!
Found your first Audio Tape

Mix Tape
Found 1/4 of the Audio Tapes

Easy Listening
Found 1/2 of the Audio Tapes

Router
Beat the best time for the Point to Point Minigame (Normal)

P2P
Beat the best time for the Point to Point Minigame (Insane)

Electrician
Beat the best time for the Polarized Circuit Minigame (Normal)

Jury Rig
Beat the best time for the Polarized Circuit Minigame (Insane)

Chromatic
Beat the best time for the Kaleidoscope Minigame (Normal)

Thinking Three Steps Ahead
Beat the best time for the Kaleidoscope Minigame (Insane)

Gear Grinder
Beat the best time for the Jigsaw Box Minigame (Normal)

Mechanic
Beat the best time for the Jigsaw Box Minigame (Insane)

Running like Clockwork
Beat the best time for the Weapon Case Minigame (Normal)

Second Amendment
Beat the best time for the Weapon Case Minigame (Insane)

Tumbler
Beat the best time for the Dial Puzzle Minigame (Normal)

Forced Perspective
Beat the best time for the Dial Puzzle Minigame (Insane)

Connect the dots…
Beat the best time for the Lights Out Minigame (Normal)

Burned Out
Beat the best time for the Lights Out Minigame (Insane)

Smooth Criminal
Beat the best time for the Lockpick Minigame (Normal)

Master Thief
Beat the best time for the Lockpick Minigame (Insane)

Silver

Putting it all together
Found all 25 puzzle pieces

Puppeteer
Found all 7 Billy Puppets

Journalist
Found all 50 Case Files

Reel to Real
Found all 20 Audio Tapes

Platinum

Congratulations
Acquired all trophies

20 Secret

http://www.ps3trophies.org/game/saw-ii-flesh-and-blood/trophies/