Here is the full list of all 16 League of Mermaids achievements.
Get all stars in Chapter 3
Complete Level 3-15: Vault of the Deep
Complete Level 3-11: Mysterious Ruins
Complete Level 3-5: The Whirling Tower
Get all stars in Chapter 2
Complete Level 2-15:Treasure Cages.
Complete Level 2-12: Tangled
Complete Level 2-8: Wheels of Wisdom
Complete Level 2-5: Pillars of Fate
Get all stars in Chapter 1
Complete Level 1-15: The Crown of Poseidon
Complete Level 1-10: The Bowl of Thunders
Complete Level 1-5: Three Bowls.
Get all stars in the Classic Puzzles mode
Reach 1000m in the Bottomless Trench
Achieve the Master Treasure Hunter rank in Zen mode.