Well, the most powerful spell to use against him is Divine Retribution, the Mercurian World spell.
Fireballs will work, but you'll need lots. Demons are resistant (although not immune) to fire damage. They are immune to Death and Unholy damage, so undead/demonic units (although these units immunity to fear could help), death summons, and the entropy 3 spell won't be effective. They are weak to holy damage. Hosts of the Einherjar are the only holy-damage summon, iirc. They also gain duration each time they kill a unit and they can get promotions, so you can kill lesser demons to level these summon up and prepare them to slay Hyborem. Angels, Crusaders, Monks, and Paladins also have holy strength, plus they start with the demon slaying promotion. When it comes time to actually kill him rather than just weaken him, I'd probably use a Paladin, since they are the strongest of these (excluding the top tier Mercurian Angel UUs, but even then I prefer a Paladin because if it loses it will return as an angel). The Empyrean High Priest/Chalid spell, Crown of Brillance, is quite effective at weakening him. The spell directly deals a considerable amount of holy damage and grant a promotion that passively casts the spell once per turn until the promotion wears off. Chalid is usually considered the best hero because he can hurt enemies with and earlier cast Crown of Brillance, then hit them with Pillar of Fire (a strong direct damage fire spell that is now unique to him), then he and his earlier summoned Einherjar (boosted by his loyalty and Valor spells) can attack.
Maelstrom is generally good for weakening foes, and this is no exception. It is a direct (lightning) damage mage (not a national unit like archmage) spell, so you can have lots of caster work together to help bring him down. Any summon with extra strength from affinity (excluding those whose affinity is only for death) can be effective with enough mana.