*UPDATE*
The mod has been updated to version 1.1. Now all songs should play long enough so you won't hear them fade out during a match, the volume has been boosted for all songs, and a few song were changed. Here's the list of  changed themes:

CHARACTERS
------------------

Goku - Ultimate Battle (Super)
     formerly An Isolated Warrior (Kai)

Goku Black - Death-Match with Goku Black (Super)
     formerly The Birth of Merged Zamasu (Super)

Gotenks - Omen of Victory (Super)
     formerly Fusion Complete (Kai)

Trunks - Hikari no WILL POWER (Dragon Ball Z)
     formerly The Lone Warrior (Kai)

Yamcha - Wolf Hurricane (Dragon Ball)
     formerly The Curtain Rises on the Battle (Kai)

STAGES
----------

Wastelands - Destiny (Kai)
     formerly The Ebb and the Flow (Kai)

West City - My 18th Magic (Kai)
     formerly Kintoun (Kai)

World Tournament - Battle Royale (Kai)
     formerly Budokai Tenkaichi (Kai)

This is just my custom soundtrack mod using the music from the animes. It primarily uses music from Kai and Super, but a there are a few exceptions. Here's the full list of songs I used:

CHARACTERS
------------------

Android 16 - A Battle of Rivalry (Kai)
Android 18 - The Braveheart Challenges the Strong (Kai)
Android 21 - Fierce Battle against a Mighty Foe (Super)
Bardock - Solid State Scouter (Father of Goku special)
Beerus - Beerus' Madness (Super)
Broly - 10's (Pantera)
Buu - Super Buu's Theme (Bruce Faulconer)
Cell - The Fierce Battle (Kai)
Freeza - Only a Chilling Elegy (Kai)
Ginyu - Sanjo!! Ginyu Tokusentai!! (Kai)
Gohan - Theme of Super Saiyan (Kai)
Goku - Ultimate Battle (Super)
Goku Black - Death-Match with Goku Black (Super)
Gotenks - Omen of Victory (Super)
Hit - Strongarm Battle (Super)
Krillin - Scampering Battle! (Kai)
Nappa - The Formidable Warrior, the Saiyan (Kai)
Piccolo - Theme of Piccolo (Kai)
Tien - The Clouds of War Spread (Kai)
Trunks - Hikari no WILL POWER (Dragon Ball Z)
Vegeta - Theme of Vegeta (Kai)
Yamcha - Wolf Hurricane (Dragon Ball)

 

STAGES
----------

Cavern - Hero ~Kibou no Uta~ (FLOW)
Cell Games - News of the Cell Games (Kai)
Island - Effective Hit (Kai)
Land of the Kai's - Super Saiyan 3 (Kai)
Planet Namek - A Mighty Foe (Kai)
Planet Namek (Destroyed)-｢F｣ (Maximum the Hormone)
Rocky - An Outcome-Switching Recovery (Kai)
Space - Instant-Kill Battle (Super)
Wastelands - Destiny (Kai)
West City - My 18th Magic (Kai)
West City (Destroyed) - Win Tough Fight! (Kai)
World Tournament - Battle Royale (Kai)

 

MENUS & LOBBY
----------------------

Title Screen - CHA-LA HEAD-CHA-LA -Instrumental- (FLOW)
Character Select - Limit-Break x Survivor (Instrumental Type A) (Super)
Results Screen - Next Episode Preview (Kai)
Versus Screen - The Strongest Enemy Has Appeared! (Kai)
Lobby - Running Across the Land (Kai)

 

Credit to MexicanBBQ for making the OST Mod Maker tool which I used to make this.

In your game directory go to "DRAGON BALL FighterZREDContentPaks" and make a folder called "~mods". Then extract the folder "AnimeOST" in to the newly created "~mods" folder.