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