Here is the full list of all 38 Ziggurat achievements.
Unlock all character classes
Kill all enemies at least once (including bosses)
Win the game without using any level up
Unlock all enemies in the bestiary
Find all lore scrolls
Get to floor 3 using only the magic wand (Apprentice class only)
Reach floor 2 without getting damaged
Find a super secret cheat code
Kill 5000 enemies
Break 2,000 things (Barrels, tombs...)
Die 10 times
You died on a danger room
Kill 500 enemies affected with elemental states
Survive the Ziggurat
Master a perk by getting it to level 5
Find a secret room
You've been ambushed in a treasure room
You met your match in the final showdown
Reach experience level 15
Kill 1000 enemies
Kill a Lost soul with the Skull of Xanatos
Reach experience level 10
Equip a weapon of every kind
You reached 3rd floor. Now the real lesson begins.
Reach experience level 5
Find your first amulet
Complete a challenge room
Get your first level up
Unlock all magic weapons
Unlock all perks
Unlock all weapons,perks,lore & character classes
Die 25 times
Die 50 times
Win a game with every character (any difficulty)
Win a game on hard difficulty
Died after killing the boss
Unlock all amulets
Win the game with Argo on Normal difficulty in less than 45 minutes