Here is the full list of all 14 Marble Duel (EU) trophies - there are 7 bronze and 7 silver.
Win the Candles mini-game
Receive 6 additional spheres in one turn
Chain of 8 hits
Deal over 60 damage points in one turn
Win a duel without using red spheres
Let the birds out of the cave
Win the Airplane mini-game
Chain of 6 hits
Receive 3 additional sphere in one turn
Win a duel before 3 of your turns were up
Win a duel before 5 of your turns were up
Destroy the Crystal of Petrification
Destroy the spheres in a moving string
Receive 12 additional spheres in one turn