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