Here is the full list of all 20 Dungeons Again achievements.
Enter the dungeon
Summon a ghost with a tombstone
Carry 250 gems
Enchant weapon using the spell table
Leave memories of yourself in the dungeons
Obtain Emrtilim - the strongest sword in the game
Use the golden key to open the golden chest
Achieve level 5
Achieve level 10
Use Skyfury - sword, that summons falling stars
Obtain Amulet of Yendor - extremely powerful artifact of unknown origin
Buy the most expensive food in the dungeons
Get to the Ice Caves - a place inhabited by evil and dangerous Ogres
Get to the Abandoned Prisons - lair of Heavy Guardians and Honey Fowls
Get to the Core - abode of Satyrs and Infernal birds
Kill the Kobold - Abandoned Prison's guard
Kill Stinger the Great - Ice Kingdom's King
Kill Master Tenno - The ancient samurai
The minotaur is dead, now the fate of the world is in your hands
Explore a hidden cave behind a waterfall