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.

Additionally, there are three secret trophies:

Mankind saved (Bronze): Complete the fifth world.
Impossible unlocked (Bronze): Complete the fifth world on "hard".
Nightmare unlocked (Bronze): Complete the fifth world on "impossible".