Here is the full list of all 12 Broken Hearts Island achievements.
Watch the prologue
Make Daisy read her diary
Dream with the blue fairy
End in Calidum
Resist the dark magic
Turn the topic to food in important choice
Ask the fairies all possible questions
Go through the entire game in special mode
Do not resist the dark magic
Protect Daisy
Ending with the new fairy
Visit Calidum twice