Here is the full list of all 17 Super Dodgeball Beats (EU) trophies - there are 4 bronze, 3 silver, 9 gold and 1 platinum.
Obtain all other trophies
Win your first tournament
Unlock all teams and mascots
You've been disqualified from a tournament
Play over 100 multiplayer matches
Win a league with a bronze medal
Complete all entries in the codex screen
Use a healing item to heal from an enemy power-up
Throw 18 power-ups or more in a single match
Steal a racoon power-up from an enemy
Conclude a match with no sides claiming victory in legendary difficulty
Achieve 100% perfect beats in a match
Get a 1000 beat combo without failing
Win over 100 matches
Win a legendary league without using any power-ups
Win your first match
Get a platinum tournament average on a legendary level match