Here is the full list of all 13 Mystic Melee achievements.
Complete the tutorial levels.
Achieve an "S" rank
Have an "A" average across Arboria.
Have an "A" average across Summitar.
Kill two birds with the same boulder toss.
Have an "A" average across the Academy.
Defeat the boss of Arboria.
Destroy 50 beetles.
Destroy 40 birds.
Find 3 Mystic Mana.
Find 8 Mystic Mana.
Find 16 Mystic Mana.
Find 24 Mystic Mana.