Here is the full list of all 33 Alchemist: The Potion Monger achievements.
Brew a Potion with Fire Aspect
Get level 5
Adopt a Salamander
Have 20 furnitures in your house
Have 10 furnitures in your house
Adopt a Cat
Loose all hearts
Defeat the Slime King
Brew a Potion with Air Aspect
Destroy all vines next to your house
Break through the vines
Earn 10.000 gold from Contracts
Discover all Earth Aspects
Discover all Fire Aspects
Discover all Air Aspects
Discover all Water Aspects
Adopt a Turtle
Discover the whole map
Defeat the Snake King
Unlock the Black Market
Brew a Potion with Water Aspect
Create a 3 star potion with 4 tier aspect
Defeat the Herbalist
Complete the main quest
Have 7 hearts (6 as a Cat)
Craft 100 potions using Enchanted Paper
Discover 50 Potion Recipes
Earn 10.000 gold from your Shop
Unlock all Portals
Save 10 Auto Potion Recipes
Get level 10
Have 30 furnitures in your house
Cheat death with Resurrect Potion