Here is the full list of all 63 Spell Disk achievements.
Survive as a Novice
Win with Danger Level 0
Win with a Staff
Survive as a Chronomancer
Survive as a Collector
Survive as a Cryomancer
Survive as a Cursed
Survive as a Deranged
Survive as a Determined
Survive as a Duplicator
Survive as a Dwarf
Survive as an Electromancer
Survive as a Gazer
Survive as a Giant
Survive as an Incantor
Survive as a Loafer
Survive as a Pyromancer
Survive as a Refresher
Survive as a Alchemist
Survive as a Rogue
Survive as a Sprinter
Survive as a Trembler
Survive as a Visionary
Survive as a Wayfarer
Survive with an Axe
Survive with a Hammer
Survive with a Katar
Survive with a Scythe
Survive with a Spear
Survive with a Staff
Survive with a Sword
Win with an Axe
Win with a Hammer
Win with a Katar
Win with a Sword
Win with a Scythe
Win with a Spear
Win with Danger Level 1
Win with Danger Level 2
Win with Danger Level 3
Win with Danger Level 4
Win with Danger Level 5
Win with Danger Level 6
Win with Danger Level 7
Win with Danger Level 8
Win with Danger Level 9
Win with a Magic Book
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