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
Forest world complete
Earned 100.000 coins
20 hints bought
50 hints used
World completed without hints
Hamlet world complete
Mini-game complete
"Solved in less, then 60 seconds"
3 levels in raw without hints
Tutorial finished