How to install:
1. Go to  \JoJo's Bizarre Adventure All-Star Battle R\data\patch
2. Replace this file: bgm.cpk (make backup in case you'd want to uninstall the mod)
And that's it!

Tracks I used in this mod for each character:
Jonathan Joestar - Fukutsu Mushin no Sakebi
Will A. Zeppeli - Capture the Target
Robert E.O. Speedwagon - Strutting The Ogre Street
Dio Brando - Decisive Battle Overlapping Destinies
Joseph Joestar - Overdrive
Caesar Zeppeli - Oh Please
Lisa Lisa - Master
Esidisi - Awaken
Wamuu - Burning Colosseum
Kars - Avalon
Jotaro Kujo - Stardust Crusaders
Noriaki Kakyoin - Noble Pope
Muhammad Avdol - Fire Shaman
Jean Pierre Polnareff - Cavalerie & Ken撃
Old Joseph Joestar - Overdrive Instrumental
Iggy - Fool of Sand 
Pet Shop - Rebellion to Despair
Hol Horse - Wind in the Wilderness
Mariah - Lady With Beautiful Legs
Vanilla Ice - Shoot Towards The Decisive Battle
DIO - Awakening Darkness of The World & Final Battle
Josuke Higashikata - Diamond is Unbreakable Main Theme
Okuyasu Nijimura - The Hand
Jotaro Kujo (Part 4) - The Kakero The Bluff
Koichi Hirose - Evolution
Rohan Kishibe - Sudden Battle
Yukako Yamagishi - Crazy in Love
Akira Otoishi - Electric Guitarist
Shigekiyo Yangu - Friends! Friends?
Yoshikage Kira - Second Bomb
Kosaku Kawajiri - Cornered
Giorno Giovanna - il vento d'oro
Bruno Bucciarati - Nella Cerniera
Guido Mista - Squadra
Narancia Ghirga - Aereo de caccia
Pannacotta Fugo - Virus
Prosciutto and Pesci - Pesce
Ghiaccio - Ghiaccio
Trish Una - Figlia
Diavolo - The Final Battle 
Jolyne Cujoh - Jolyne's Theme
Ermes Costello - Groovy Cells
Foo Fighters - Zero Gravity
Narciso Anasui - Pucci's Plan
Enrico Pucci - Pucci's Theme

For some characters like Rohan, Ermes, F.F and Anasui I didn't use their main themes because they didn't fit for a fighting game, so I used tracks that played during their combat scenes in the anime. There's no Risotto because I do not own the dlc yet