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