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