Here is the full list of all 17 Little Briar Rose achievements.
Don't use hints in the second maze puzzle.
Don't use hints in the first maze puzzle.
Finish the game with the second prince (Stephen).
Listen to all of Navi's advices.
Kiss the Princess with the wrong prince.
Die seven times.
Don't use hints in the third maze puzzle.
Finish the game once.
Finish the game with the first prince.
Don't use hints in the fourth maze puzzle.
Help the Spriggan date the Fairy.
Collect every item.
Obtain a Perfect result in the cooking game.
Obtain a Perfect result in the sewing game.
Capture the Golden Fish.
Choose the right decoration for the Gnomes' house.
Die three times in the same puzzle.