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