Here is the full list of all 50 Love Tavern achievements.
Build a shop
Build a single dormitory
Build a single dining room
Build a single hunting room
Earn 7777 gold
Hire a staff member
Welcome Izumi to the tavern
Welcome Nozomi to the tavern
Welcome Flann to the tavern
Welcome Leona to the tavern
Complete 4 chapters of Izumi
Build a massage room
Build a single sauna room
Build a single onsen room
Build a single cleaning room
Build a single storage room
Build 40 of any type of room
Collect 1mil Gold
Collect 1000 ingredients
Cook 600 dishes
Cook 120 perfect dishes
Provide 100 massage services
Provide 100 sauna services
Provide 100 onsen services
Learned 20 cooking recipes
Clean 100 times
Complete dungeons 50 times
Served 1500 customers
Hire 30 staff members
Hire 1 five-star staff member
Hire 10 five-star staff members
Welcome Miwa to the tavern
Welcome Natsumi to the tavern
Welcome Tamiko to the tavern
Welcome Toyo to the tavern
Welcome Lilith to the tavern
Welcome Nadia to the tavern
Welcome Emily to the tavern
Complete 4 chapters of Nozomi
Complete 4 chapters of Miwa
Complete 4 chapters of Natsumi
Complete 4 chapters of Tamiko
Complete 4 chapters of Toyo
Complete 4 chapters of Flann
Complete 4 chapters of Lilith
Leona's story
Complete 4 chapters of Emily
Welcome Slyvia to the tavern
Welcome Sakura to the tavern
Hire all unique staffs to the tavern