After the fight, the Void begins to devour Exdeath, transforming him into Neo Exdeath.
In the GBA version and beyond, both Exdeath and Neo Exdeath can be beaten with a single party member. Using the Freelancer job with Rapid Fire, while dual-wielding two Blood Swords, and sporting a Ribbon, and the party's best armor; when combined with enough HP, this setup will allow the character to keep their HP up.
In the GBA version, Exdeath can be defeated by using either the Chaos Cannon (Dark Matter and Blitzshot) or the Dark Cannon (Ash and Blitzshot) to deplete the last of his health. (One should monitor it and use when near 2,000 health.) Exdeath will be defeated without having to fight Neo Exdeath. This trick does not work in the mobile or Steam versions.