Here is the full list of all 22 Spellspire achievements.
Descend to dungeon level 10.
Complete star challenges for each of the floors.
Buy all hats.
Reach 150m distance in the dungeon.
Slay the dragon at the top.
Find 25% of the available words in a level.
Upgrade the luminous robe to maximum level.
Upgrade a legendary wand to maximum level.
Beat the Prince on 80th floor.
Beat the Royal Jelly on 70th floor.
Beat the Lard Corpse on 60th floor.
Come up with a ten letter word without using dictionary books.
Beat the Ballistic Gel on 50th floor.
Beat the Goblin on 40th floor.
Beat the Carp Knight on 30th floor.
Come up with an eight letter word without using dictionary books.
Come up with a nine letter word without using dictionary books.
Beat the Unicorpse on 20th floor.
Come up with a seven letter word without using dictionary books.
Beat the Armored Corpse on 10th floor.
Descend to dungeon level 42.
Slay the chrome dragon in the dungeon.