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

Getting out more (Bronze): Play online at least once.
Don't need no stinking powerballs (Bronze): Win without using a powerball, but you can still pick them up.
Variety is the spice of life (Bronze): Win at least once in all game modes, including one online multiplayer match.
Comeback kid (Bronze): Come back and win a game from 3 goals behind.
Use your emotions (Bronze): Win at least once with each powerball.
Leagues ahead (Bronze): Win at least once in all 4 divisions.
You're a winner (Bronze): Win 10 games in a row.
Gimme gimme world domination (Silver): Win 50 online games.
Mini game master (Silver): Complete all 8 mini-games.
League of your own (Silver): Win the top division three times in a row.
Completist freak (Silver): Get 100% on time attack mode.
Geon king (Gold): Score 200,000 points to be a Geon king.