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