Here is the full list of all 15 Rakuen achievements. It takes around 10-12 hours to unlock all of the achievements on Windows.
Complete the game.
Collect and place all the special items for the hospital.
Learn 'Mori no Kokoro' Part 5.
Collect all the jukebox tracks.
Adopt all the pets.
Help the Wooden Sign on Wooden Sign Day.
Discover the Leeble Protection Agency.
Learn 'Mori no Kokoro' Part 4.
Return all of Sue's marbles.
Learn 'Mori no Kokoro' Part 3.
Examine each unique piece of Monsieur Bud themed artwork.
Learn 'Mori no Kokoro' Part 2.
Learn 'Mori no Kokoro' Part 1.
Become Radical in the eyes of the Radshroom Protection Society.
Help save Bad Attitude Onion from his bad attitude.