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