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