One of the menus inside the farmhouse bookshelf is a list of Achivements you can earn. There are a total of 35 goals you can complete. The in-game achievements don't unlock special features once completed. They're basically there for you to complete if you choose to do so.
The Steam achievements are the same as the in-game Switch achievements.
In the Japan version of the game, meeting the criteria to unlock an achievement in one save file will unlock that same achievement in other save files, like they are a global game achievement rather than an individual game achievement. It is unknown if this is also true in the EN/EU versions of the game.
1. Happiness is Eternal
You can earn this achievement by getting married.
2. My New Life
This achievement unlocks automatically on Spring 1 of your second year.
3. Farm Life Forever
Same as above, but unlocks on Spring 1 of your third year.
4. Agriculture, I Am Thy King
The last one in this chain automatically unlocks on Spring 1 of your fifth year.
5. No Ulterior Motives, I Swear
Toss a total of 300 gifts into the Goddess' pond. Only the first gift you throw into her water each day will count towards this achievement.
6. A Comfortable Living
Have at least 50,000 G on hand to unlock this achievement.
7. Time to Start Investing
Have at least 100,000 G on hand.
8. Now I can Retire Early
Have at least 5,000,000 G on hand. Note that the Switch version has an error where it states you only need 500,000 on hand.
9. Grade-A Fisher
Catch at least 10 species of fish when fishing.
10. Master Angler
Catch at least 50 species of fish.
11. Caught the Guardians
Catch all species of fish in the game. There are a total of 57 fish in the game: 50 normal fish and 7 whopper fish.
12. I Cooked and Didn't Burn it!
Successfully cook 10 different recipes using your kitchen.
13. Home Cooking is my Hobby
Successfully cook 50 different recipes using your kitchen.
14. Bon Viviant's Successor
Successfully cook all recipes in the game. There are a total of 120 cooking recipes to collect and craft. You'll receive a letter in the mailbox from the Harvest Goddess when you meet this requirement.
15. A Little Adventure
Reach level 30 in either the spring mine or the lake mine.
16. My Real Job is Spelunking
Reach level 100 in either the spring mine or the lake mine.
17. Gaze Into The Abyss
Reach level 255 in either the spring mine or the lake mine.
18. Let's Impress Zack
Ship at least one of each field crop in the game, regardless of star rank. Flowers aren't included in this achievement, even though you can technically grow them on your farm. Tree fruit also aren't field crops.
19. All Natural, Non-GMO
Ship at least 1 of each crop in the game that has a 5-Star rank. Flowers and fruit trees don't have star rank.
20. Master Cow Rancher
Have a total of 8 cows living on your farm (any combination of normal, fruit, coffee, and strawberry) at the same time.
21. Master Sheep Rancher
Have a total of 8 sheep living on your farm at the same time. You can buy the sheep from Mugi, unlock the achievement, and then simply sell the unwanted sheep back to Mugi.
22. Master Chicken Keeper
Have a total of 4 chickens living on your farm (any combination of white or brown birds) at the same time.
23. Master Rabbit Keeper
Have a total of 4 rabbits living on your farm at the same time.
24. Master Alpaca Rancher
Have a total of 8 alpaca living on your farm at the same time. You can use the same trick here as you can with the sheep. Mugi doesn't mind.
25. Why Pick Only One?
Have at least 1 of each species of animal living on your farm: chicken, rabbit, alpaca, sheep, cow, coffee cow, strawbery cow, and fruit cow.
26. Master Breeder
Have a birth/hatch of each type of animal family. In this achievement, the cows all count for the same type of animal. You don't need to breed all four cow species; just one of them.
27. Solomon's Ring
Own 5 pets. Van the traveling merchant will sell pets in Rose Plaza on the 15th of every season. To buy additional pets, the existing pets you own need to have at least 8 hearts of friendship. The horse does not count as one of these pets.
Some Switch players haven't got this to unlock, though Steam players are a-okay.
28. Titan of the Clash
Win the Summer 7 Cluck-Cluck Clash chicken sumo contest for the first time.
29. Grade-A Quality
Win the Summer 20 Moo-Moo cow festival for the first time.
30. Eat My Shorts, Yodel Ranch
Win the Autumn 21 Fluffy Festival for the first time.
31. A Full House
Upgrade your farm house to its largest size. You don't need to build the optional components like the window and mailbox remodels or the bathroom.
32. Funding Gotts' Retirement
Have Gotts build all the building upgrades on your farm such as the fodder holders, barns, and so on.
33. Talk About Prune Skin
Use the hot spring for a total of 10 hours in one sitting. Exiting the hot spring will reset the timer.
34. Home Cooking Tastes Best
Successfully eat all of the edible recipes you can make in your kitchen. The seasonal suns that you can cook in the kitchen are not edible. You don't have to eat the unique town shop meals. The Harvest Goddess will send you a letter in the mailbox too.
35. I Choose You!
Give the Preserved Flower to all of the available marriage candidates before you get married, and then pick one to get married to. Bon Viviant, Harvest Goddess, Huang, and Kappa are not counted in this achievement because they don't have romantic heart events and cannot accept a Preserved Flower. If you have met the requirements, this achievement will unlock after your wedding, hence the "I choose you" portion of the achievement.