Here is the full list of all 28 Staxel achievements.
The base game contains 23 achievements, and there is 1 DLC pack containing 5 achievements.
Shear a Sheep 100 times
Milk a Cow 100 times
Gather 100 Mushrooms
Catch one of every fish
Catch one of every bug
Plant 1000 Seeds
Bake one of each Pie
Catch 100 Fish
Catch 100 Bugs
Sweep a ball
Gather 100 Shells
Mine 1000 Raw Stone
Reap a Gold Seed
Bake one of each Cake
Cook one of each Preserve
Cook one of each Soup
Loot a forest treasure chest
Find 100 Mixed Seeds
Use a wardrobe to change your outfit!
Throw a ball
Chop 1000 Raw Wood
Harvest Star Jelly
Deliver your farm registration letter to the mayor
Catch one of each bug found on the Galaxy Island.
Catch one of each fish found on the Galaxy Island
Cook Couscous and Baked Artichoke with Goats Cheese
Harvest Grapes, Artichokes, Purple Nettle and Rhubarb
Collect Goats Milk and Brown Pheasant Feathers