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