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