Here is the full list of all 19 Marble Duel achievements.
Win the Candles mini-game
Win a duel without using red spheres
Win the Cave mini-game
Kill all the crows in the Airplane mini-game
Win the Airplane mini-game
Destroy the spheres in a moving string
Chain of 6 hits
Deal over 30 damage points in one turn
Deal over 60 damage points in one turn
Win the Roulette mini-game
Chain of 4 hits
Win a duel before 10 of your turns were up
Win a duel before 5 of your turns were up
Win a duel before 3 of your turns were up
Win the first duel
Receive 3 additional sphere in one turn
Chain of 8 hits
Receive 6 additional spheres in one turn
Receive 12 additional spheres in one turn