There are 12 Trophies that can be collected.

Bronze

Copter Rider    
Have a snack on the Petit-Copter!    

Shameful    
Lose rock-paper-scissors even while using a Telepathy Ball.    

Petit-Copter    
Enjoy a sky cruise in the Petit-Copter.    

Rockin' the Bike    
Ride through Stage 2 on the Sukopako Motorcycle.    

Fists of Stone    
Break 300 blocks with your fists.    

Octopus Sushi    
Defeat both giant octopi.    

A Brush with Death    
Outrun a ghost!    

Tears of Regret    
Run out of lives in Janken's dungeon with less than $400.    

Good Vibrations    
Freeze in fear from breaking a Skull Block.

Silver

Mission Complete    
Clear every stage.    

Boat Cruise    
Clear Stage 9 while on the Suisui Boat.

Gold

Amazing Score    
Collect all the items and finish the game.

http://www.ps3trophies.org/game/alex-kidd-in-miracle-world/trophies/