Here is the full list of all 43 Fae Farm achievements.
The base game contains 35 achievements, and there is 1 DLC pack containing 8 achievements.
Bring all Skills to Level 20.
Catch 200 Fish
Get pulled underwater...
Have a House With Maximum Coziness.
Witness a Second Year in Azoria.
Complete the Final Chapter of the Story.
Complete the Seventh Chapter of the Story.
Find 100 Scattered Scrolls.
Fully Upgrade your Tools
Catch 500 Critters
Have Your First House Fully Upgraded.
Earn 100,000 Florins
Complete the Sixth Chapter of the Story.
Bring one Skill to Level 20.
Get Married.
Complete the Fifth Chapter of the Story.
Make Friends with 10 Azorians at a time.
Smash 500 jumbles.
Harvest a Hybrid Flower.
Harvest 500 Vegetables.
Collect 200 Shells and Coral Along the Beach.
Complete the Fourth Chapter of the Story.
See That 30 Shade Clouds are Chased Away.
Catch 2 or more critters with one swipe.
Chop and Collect 400 Logs
Complete the Third Chapter of the Story.
Cook 200 Meals.
See That 50 Thorns are Destroyed.
Find 50 Scattered Scrolls.
Pick and Collect 400 Minerals
Complete the Second Chapter of the Story.
Complete the First Chapter of the Story.
Gather 100 Wild Four Leaf Clovers.
Complete 10 shipping contracts.
Complete all the Job Quests.
Coasts of Croakia: Have 50 unique critters follow you after befriending them with the critter conch.
Coasts of Croakia: Pick up 20 of the scrolls hidden all over Archi-Pal-igo Park.
Coasts of Croakia: Become a master of the critter conch and learn 5 critter languages.
Coasts of Croakia: Jump into 100 of the dewdrops found in lilypads scattered around Archi-Pal-igo Park.
Coasts of Croakia: There are 16 critter types that are unique to Archi-Pal-igo Park, catch 50 of them.
Coasts of Croakia: Jump onto Grenu's lilypad hat.
Coasts of Croakia: Find the hole in the island and fall through into the cave below.
Coasts of Croakia: Acquire and Equip any Superior Trinket onto your critter companion.