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
Bake one of each Pie
Bake one of each Cake
Cook one of each Soup
Cook one of each Preserve
Gather 100 Mushrooms
Catch one of every fish
Sweep a ball
Throw a ball
Reap a Gold Seed
Catch one of every bug
Use a wardrobe to change your outfit!
Find 100 Mixed Seeds
Catch 100 Fish
Plant 1000 Seeds
Loot a forest treasure chest
Catch 100 Bugs
Gather 100 Shells
Mine 1000 Raw Stone
Chop 1000 Raw Wood
Harvest Star Jelly
Deliver your farm registration letter to the mayor
Harvest Grapes, Artichokes, Purple Nettle and Rhubarb
Collect Goats Milk and Brown Pheasant Feathers
Catch one of each fish found on the Galaxy Island
Catch one of each bug found on the Galaxy Island.
Cook Couscous and Baked Artichoke with Goats Cheese