There are 48 Trophies that can be collected.

Bronze

Super Trooper    
Complete Act 1 on any difficulty level     

Determined Do-gooder    
Complete Act 2 on any difficulty level         

Intrepid Adventurer    
Complete Act 3 on any difficulty level     

Fearless Front-Facer    
Complete all chapters on Normal

Sizzling Century Mark    
Defeat 100 enemies

Gorgeous Gold Grabber    
Web of Challenges – Obtain All Gold Medals for a Chapter

Ambitious Arachnid Acquirer    
Obtain 1/4 of the Golden Spiders     

Superb Spider Searcher    
Obtain 1/2 of the Golden Spiders

Alchemaxed Out!    
Buy all Combat Upgrades     

Gold Standard    
Buy all Character Upgrades     

Super-Suited Swinger    
Obtain all Alternate Suits     

Furious Fist Fighter    
Execute a 50-hit combo     

Hundred Hit Hero    
Execute a 100-hit combo     

Infinite Slugger    
Execute a 200-hit combo     

Fantastic Five Hundred    
Collect 500 Orb Fragments

Survivor Supreme    
Complete Session 3 or later without dying     

Jack Of All Attacks    
Perform 3 of each type of Grab Attack on enemies     

Airborne Assailer    
Perform 3 of each Air Attack on enemies     

Hammer Slammer    
Damage enemies with Roundhouse Spin and Web Hammer 10 times each

Silver

Master Of All You Survey    
Complete all chapters on Hard

Spider Slugger Supreme    
Defeat 500 enemies

Mighty Medal Master    
Web of Challenges – Obtain All Gold Medals for an Act

Excellent Emblem Enthusiast    
Collect 1000 Orb Fragments     

Collector Detector    
Collect 2000 Orb Fragments

Gold

Consumate Completist    
Web of Challenges – Obtain All Gold Medals

Spider Snagger Supreme    
Obtain all Golden Spiders

Platinum

Spider-Man™: Edge of Time Platinum    
Unlock all trophies to earn this.

21 Secret

http://www.ps3trophies.org/game/spiderman-edge-of-time/trophies/