You don't know how happy this comment makes me!! Thank you so much for playing through Devil Catcher with both perspectives!!
The music is not original it is from a website called Artlist but you can find all songs on Spotify and probably Youtube
The songs are listed here:
Main menu: My Reasons Have Changed - Jamie Bathgate
Level 1: Pink Flamingo - Ace
Devil Boss: Data 80 - Stefano Mastronardi
Level 2: Thirds - Jamie Bathgate
God Boss: Data 80 - Stefano Mastronardi