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