Here is the full list of all 21 The Spellswapper achievements.
Unlock the Druid
Unlock the Mystic
Unlock the Enigma
Win a Daily Run
Win the Daily Run three days in a row
Win a run at ascension 1
Win a run at ascension 5
Win a run at ascension 10
Win 3 runs as the Wizard, unlocking all the Wizard's items
Win 3 runs as the Druid, unlocking all the Druid's items
Win 3 runs as the Mystic, unlocking all the Mystic's items
Win 3 runs as the Enigma, unlocking all the Enigma's items
Obtain a Legendary spell
Unlock the Elder
Win 3 runs as the Elder, unlocking all the Elder's items
Unlock all characters and items
Activate a synergy by obtaining 3 spells of the same element
Obtain the first item by beating wave 5
Defeat 500 enemies
Defeat 1000 enemies
Defeat 2500 enemies