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

  Back Then (Gold): You've cleared all the stages with "Back Then Katamari 
  Damacy". 
  Big Katamari (Bronze): Create a Katamari which is over 500m. 
  Big, Big Katamari (Bronze): Create a Katamari which is over 10,000km. 
  Big, Big, Big Katamari (Silver): Create a Katamari which is over 2,000,000km. 
  Collector (Gold): You've collected all of the Presents. 
  Congratulations (Gold): You've cleared all the stages with "New Katamari 
  Damacy". 
  Cousin Mania (Gold): You've collected all of the Cousins. 
  Creator (Silver): Make over 200 Katamaris. 
  D-d-d-d-d-dash (Bronze): Complete a stage using "Oji Dash" only 6 times. 
  Destroyer (Silver): Throw at least 50 Katamaris away. 
  Falcon (Gold): You've cleared all stages with "Katamari Drive". 
  Fashionable (Bronze): Collect over 30 varities of Presents. 
  Film Fan (Bronze): Watched over 5 films in Film Mode, without skipping. 
  First Katamari (Bronze): You have completed the first stage. 
  First Star Of Rubbish (Bronze): You have thrown away your first Katamari Star.