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