Here is the full list of all 22 Everdream Valley achievements.
Pet 5 animals
Train your dog to the maximum level
Cut down 5 trees
Catch 30 butterflies
Catch 5 fish
Catch 30 fish
Prepare 5 dishes
Prepare 30 dishes
Collect all species of animals on the farm
Raise one young animal
Raise 20 young animals
Collect 100 mushrooms
Harvest crops from 50 plants
Harvest the crop from 300 plants
Go through one dream mission
Go through 10 dream missions
Pet 30 animals
Play with the cat until it reaches the maximum level
Cut down 30 trees
Raise a chicken
Raise 20 chickens
Find 3 magpie nests