Here is the full list of all 16 League of Mermaids achievements.
Get all stars in the Classic Puzzles mode
Reach 1000m in the Bottomless Trench
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.
Achieve the Master Treasure Hunter rank in Zen mode.