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