There are 12 Trophies that can be collected.

Bronze

SEGA Games Are #1!    
Watch the SEGA logo sequence.    

Monster World Welcomes You    
Find the "Welcome to Monster World" message.    

Refreshment    
Wash your face in the spring at the Pyramids.    

Be a Bit More Careful    
Just started and you're already falling in pits!    

Such Agility    
Land 3 consecutive downthrusts without touching the ground.    

Happy Earth Spirit    
Rescue the Earth Spirit.    

Thankful Moon Spirit    
Rescue the Moon Spirit.    

Delighted Sun Spirit    
Rescue the Sun Spirit.    

Cute Wind Spirit    
Rescue the Wind Spirit.

Silver

Jackpot    
Collect 777 gold and see what happens.    

Every Last Drop    
Collect all the Life Drops.

Gold

You Did It!    
Finish the game.

http://www.ps3trophies.org/game/monster-world-iv/trophies/