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