Here is the full list of all 17 Super Sunny Island achievements.
Get 25 goodies.
Get 50 goodies.
Get 100 goodies.
Get 15 special coins.
Get 30 special coins.
Get 45 special coins.
Get 65 special coins.
Get 85 special coins.
Defeat the first Boss.
Defeat the second Boss.
Defeat the third Boss.
Defeat the fourth Boss.
Defeat the fifth Boss.
Defeat 25 enemies.
Defeat 50 enemies.
Defeat 100 enemies.
Defeat 200 enemies.