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