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