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