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