Beelzebub resists all elements. He can cast Fira and Firaga and inflict multiple status ailments, but he primarily uses physical attacks. His most powerful attack is Fall of Angels. After rising into the air for two turns, he falls and deals significant damage to all party members, as well as himself.
An Elementalist is not as necessary for Beelzebub as for the other Demon Lords, but Mysterio is still useful for mitigating his Fire spells if the party does not have Flame Shields equipped. It is advisable to have the Lux spell first to boost the party's stats and HP for Beelzebub's Fall of Angels, as that is the greatest danger. An unprepared party can easily be wiped out by this attack.
The party's damage-dealers should conserve AP for when Beelzebub rises into the air while the support members heal and buff. A Black Mage should use Magic Might or be equipped with Leaf spells to circumvent Beelzebub's elemental defenses, and use Magic Mojo and Spell Focus. Once Beelzebub rises to charge up Fall of Angels, the party should attack him with its most powerful techniques. It takes 300 - 400 damage to break Fall of Angels. If successful, Beelzebub will fall early and use "Bazeteor", which only damages himself.
Repeating this pattern steadily should defeat Beelzebub quickly, as Bazeteor deals around 600 damage to Beelzebub each time.