Here is the full list of all 15 T-Kara Puzzles achievements.
Reach 100 000 scores
Create 10 cross patterns in a single game
Complete a picture puzzle
Get a X5 combo
Reach 50 000 scores
Get a x8 combo
Have 5 locks on the screen at the same time.
Create ten square patterns in a single game
Crack a skull block
Complete ten picture puzzles
Get silver or more on 5 picture puzzles
Get gold on 5 picture puzzles
Win a battle
Win 10 battles