Here is the full list of all 24 Catana achievements.
You completed a level without losing a single life: 15
You completed a level without losing a single life: 50
You completed a level without losing a single life: 90
You defeated the Snapdragon: 1
You defeated the Snapdragon: 2
You defeated the Snapdragon: 3
You defeated the Sugar Joker: 1
You defeated the Sugar Joker: 2
You defeated Captain Takoyaki: 1
You defeated Captain Takoyaki: 2
You defeated the Titan: 1
You defeated the Titan: 2
You defeated the Invader: 1
You defeated the Invader: 2
Matches made during one turn: 5
Matches made during one turn: 7
Matches made during one turn: 8
Enemies defeated while playing one level: 100
Enemies defeated while playing one level: 230
Enemies defeated while playing one level: 350
Total number of enemies defeated: 1000
Total number of enemies defeated: 5000
Total number of enemies defeated: 10000
You lost a level