NOOO! WHY!? The Void was mine to command! How could it- Uwaaah!!!
For an easy battle, the party should have an average level of 40 or above. The Gladiator's (Final Fantasy V Advance and mobile/Steam versions only) Elemental Attacks can make things quicker, as well as high-level spells like Holy, Flare, and Meteor. Another popular strategy involves at least one Freelancer with the Rapid Fire and/or Spellblade command, with two weapons equipped at once. One should be ready to use some Gold Needles and Phoenix Downs, because Exdeath tends to use White Hole.
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.
In the SNES and PlayStation versions, if one mixes a Maiden's Kiss and a Holy Water on Exdeath (see Kiss of Blessing bug), it will cause him to go into Berserk and only use physical attacks, so one should make sure to have Golem. This will also end the battle after Exdeath, and the player will not fight Neo Exdeath.