Here is the full list of all 39 Dungeons of Clay achievements.
Beat level 1
Obtain a gold card
Activate any ancient stone
Complete the tutorial
Unlock the unusual gold chest
Beat area 1 boss
Collect 5 items
Kill 50 bugs
Play Chance
Play Chance 25 times
Start the 5th run
Collect 10 items
Unlock the unusual gun chest
Beat area 2 boss
Collect 20 items
Buy any of the available items in a shop
Unlock the unusual item chest
Beat area 3 boss
Start the 15th run
Have 4 companions follow you
Start the 30th run
Unlock the unusual ally chest
Unlock all ancient stones
Unlock all unusual chests
Unlock all camp items
Buy all area 1 camp items
Buy all area 2 camp items
Buy all area 3 camp items
Open a legendary chest
Open a cursed chest
Use any of the vending machines
Regenerate HP at the fountain
Go through the random door
Beat area 1 boss on hard mode
Beat area 2 boss on hard mode
Beat area 3 boss on hard mode
Win the game
Win the game on hard mode
Unlock all achievements