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