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

Marbleball Badge (Bronze): Complete Sky World level 3. 
Metalball Badge (Bronze): Complete Ice World. 
Powerball Badge (Bronze): Complete Cave World. 
Speedroller Rookie (Bronze): Collect 1 silver medal. 
Speedroller Trainee (Bronze): Collect 12 silver medals. 
Speedball Medal (Bronze): Win 5 matched multiplayer races. 
Spyglass (Bronze): Find 3 hidden paths. 
Airball Badge (Silver): Complete Lava World. 
Speedroller Expert (Silver): Collect 24 silver medals. 
Friendball Medal (Silver): Complete all cooperative levels. 
Honor Medal (Silver): Win 10 matched multiplayer races. 
Speedroller Master (Gold): Collect a Gold Medal on All levels.