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