Here is the full list of all 63 Spell Disk achievements.
Win with a Magic Book
Survive with a Hammer
Survive as a Gazer
Survive as an Incantor
Survive as a Sprinter
Survive as a Trembler
Survive with a Staff
Survive with a Spear
Survive with a Sword
Survive with a Katar
Survive with an Axe
Survive as a Visionary
Survive as an Electromancer
Survive as a Refresher
Survive as a Giant
Survive as a Loafer
Survive as a Cursed
Win with Danger Level 9
Survive as a Alchemist
Win with Danger Level 8
Win with Danger Level 7
Survive as a Dwarf
Win with a Staff
Survive as a Cryomancer
Win with Danger Level 6
Win with an Axe
Survive as a Determined
Win with Danger Level 5
Win with a Hammer
Survive as a Pyromancer
Survive with a Scythe
Win with a Scythe
Win with Danger Level 4
Survive as a Deranged
Survive as a Chronomancer
Survive as a Rogue
Survive as a Duplicator
Survive as a Collector
Win with a Spear
Win with Danger Level 3
Survive as a Wayfarer
Win with Danger Level 2
Survive as a Novice
Win with Danger Level 1
Win with a Sword
Win with a Katar
Win with Danger Level 0
Win with 28 items equipped
Win without expanding a item slot
Listen to the administrator in Imperial Palace
Stay alive for 5 minutes in Arena
Climb over 30 floors in infinity dungeon
Defeat the Dungeon Architect three times
Defeat all Grotto bosses
Defeat all Crypt bosses
Defeat all Barrack bosses
Open the gate to the Summoning Chambers
Buy all three items in the shop
Win with a Scepter
Survive with a Scepter
Survive with a Magic Book