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