(Is this what happens when ones loses all hope, body, and soul?)
Beelzebub can cast the level 3 elemental magic spells, Firaga, Blizzaga and Thundaga, and occasionally Flare, which will one-shot a character at that point in the game. It can also cast Confuse and Pig on the whole party, use Blink to nullify two physical attacks, cast Haste to increase its speed, and Tornado to reduce a target to single-digit HP.
Beelzebub is weak to Throw-elemental weapons, so Kain's Jump ability and any other attacks with spear or boomerang weapons will deal extra damage to him. A Black Mage should attack with its strongest spells, and other party members can use the strongest Bands available. A White Mage should be kept on standby to heal if anyone is hit by Tornado, or revive if they are hit Flare.
An alternate strategy, if one has two or more White Mages with the spell in the party, would be to cast Reflect on the whole party, so Beelzebub will be reflecting his damaging spells back at himself. This will also prevent anyone from being hit by Confuse or Tornado.
Beelzebub means "Lord of the Flies" in Hebrew and is a name often associated with the devil. It appears in the book by William Golding of the same name (Lord Of the Flies) as the head of a slaughtered pig on a stake. Beelzebub is also one of the Seven Princes of Hell, associated with the deadly sin of Gluttony.