Here is the full list of all 16 Picross Fairytale achievements.
All Trophies collected
Castle world complete
50 hints used
Earned 100.000 coins
All mini-games complete
All keys collected
Mountain world complete
Lake world complete
Forest world complete
20 hints bought
World completed without hints
Hamlet world complete
Mini-game complete
"Solved in less, then 60 seconds"
3 levels in raw without hints
Tutorial finished