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