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 bug
Gather 100 Mushrooms
Milk a Cow 100 times
Reap a Gold Seed
Shear a Sheep 100 times
Plant 1000 Seeds
Catch one of every fish
Bake one of each Pie
Cook one of each Preserve
Bake one of each Cake
Cook one of each Soup
Catch 100 Fish
Catch 100 Bugs
Find 100 Mixed Seeds
Use a wardrobe to change your outfit!
Sweep a ball
Loot a forest treasure chest
Throw a ball
Mine 1000 Raw Stone
Gather 100 Shells
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