Here is the full list of all 16 Dungeon Merchant achievements.
Reach Level 20 of the Dungeon
Level up a hero to level 10
Kill 100 Beasts
Kill 100 Ghosts
Kill 100 Skeletons
Kill 100 Demons
Kill 1000 Enemies
Spend 10,000G on items
Have one of each hero type in your roster
Complete all customer requests in a 4 day period
Fully upgrade your shop
Sell 1000 items
Pet Hector 100 times
Fully upgrade the gold miner
Purchase all cosmetic upgrades
Complete the story and unlock survival mode