Here is the full list of all 14 Purino Party achievements.
Clear Konoka's route
Clear Kagari's route
Clear Hinako's route
Complete all the Pure Girl routes and reach the halfway point
Clear Suzu's route
Perform a 12-chain combo during a puzzle game
Clear Yogiri's route
Clear Miyako's route
Clear Sora's route
Finish reading the opening scene
Start the game
Clear Kanae's route
Finish reading the ending scene
Complete every girl's route without ever lowering the difficulty