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