Successfully complete one of the following tasks to get a trophy:

Kettenfahrzeug destroyed (Bronze): Complete the first world. 
Windgeist defeated (Bronze): Complete the fourth world. 
Top Scorer (Bronze): Reach a score of 2,000,000. 
Combo Mania (Bronze): Complete an accumulated total of 3,000 chains. 
Master the Menace (Bronze): Complete the second world on Rank "S". 
Destroyer (Bronze): Kill an accumulated total of 50,000 enemies. 
Hidden Passage (Bronze): Collect at least four keys in each world. 
Fierce Fighter (Bronze): Play for five minutes without losing any health. 
Ultimate Key Collector (Silver): Collect all 20 secret keys. 
Galaxy Superstar (Gold): Reach ultimate rank 15: Galaxy Superstar.