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