The official website for Catherine has been updated to include looks at two aspects of the game: Jukebox and Rapunzel.
Rapunzel is the mini game which is a miniature version of the title's action stages. Your task is to reach the princess by climbing a tower, pushing and pulling blocks along the way to form steps. It has 50 stages, and you must avoid pesky bats along the way. This has been detailed before.
Jukebox, is exactly what it sounds like. When you access it, you will be able to play the game's music as well as tunes from Persona 4, Persona 3, Persona Portable, Shin Megamitensei Nocturne, and Shin Megami Tensei: Digital Devil Saga 2.
Players can access both the mini game and the Jukebox through the in-game bar, Stray Sheep.
Here's video previews of both below.