There are 12 Trophies that can be collected.

12 Secret

Bronze

Tales High 5    
Achieve a top 5 local high score on Tales of the Arabian Nights®

Ripley's High 5    
Achieve a top 5 local high score on Ripley's Believe it or Not!®

Theatre High 5    
Achieve a top 5 local high score on Theatre of Magic®

Black Hole High 5    
Achieve a top 5 local high score on Black Hole™

Silver

Tales Master    
Complete the Standard Goals on Tales of the Arabian Nights®    

Tales Wizard    
Complete the Wizard Goals on Tales of the Arabian Nights®

Ripley's Master    
Complete the Standard Goals on Ripley's Believe it or Not!®    

Ripley's Wizard    
Complete the Wizard Goals on Ripley's Believe it or Not!®

Theatre Master    
Complete the Standard Goals on Theatre of Magic®    

Theatre Wizard    
Complete the Wizard Goals on Theatre of Magic®

Black Hole Master    
Complete the Standard Goals on Black Hole™    

Black Hole Wizard    
Complete the Wizard Goals on Black Hole™

http://www.ps3trophies.org/game/the-pinball-arcade-vita/trophies/