Here is the full list of all 21 Before the Echo achievements. It takes around 10-12 hours to unlock all of the achievements on Windows.
Learn all spells.
Synthesize every recipe in the game.
See the hidden ending.
Synthesize Iridium.
Beat the game on any difficulty.
Defeat an enemy on the seventh floor using only Arclight.
Obtain every droppable item in the game at least once.
Discover the name of she who controls fate.
Defeat an enemy using only poison spells.
Defeat an enemy within eleven seconds.
Get her back.
Queue up five spells in a row.
While learning a spell, achieve 100% accuracy for the entire song.
Trigger Boost a Trigger Boost.
Defeat an enemy with less than one second remaining on the clock.
Successfully complete a synthesis at 25% odds of success or lower.
Recover over 150 mana in a single battle, and win.
Defeat the Holiday Whompa.
Obtain all three droppable items from any single enemy.
Successfully defeat your first enemy.
Complete a battle without failing a spell.