Here is the full list of all 14 Doll Explorer achievements.
Start the game
Finish the tutorial
Defeat Lamia in the forest
Defeat Lamia in the cave
Defeat Lamia in the abyss
Defeat the final enemy
Ordered all the meals
Using the elixir of mana
Defeat Slime Girl
Defeat Lava Girl
Defeat Acid Girl
Get the book of White Lily and Black Lily
Enhance all magic
Buy back all facilities