Here's a the strategy to put Belphegor in his place.

Characters, Crowns, Stats and Abilities

• Brandt (Ranger) - The only reason I have him as a ranger is because he's my strongest character with a bow (fully upgraded in Urbeth). You can use him as a White Mage (recommended if you're having trouble) but he needs the Cure and Raise spell.
• Jusqua (Black Mage) - VERY IMPORTANT!!! Jusqua needs only three spells without one, it is impossible to win this fight; Blizzard, Aero, and Fire magic are NECESSARY!!! If you're feeling lucky with your AP amounts, bring the -ga versions of the spells (Firaga, Blizzaga, and Aeroga).
• Yunita (Bard) - She needs to have leveled up the Bard crown at least once so she has Motet and Ditty (I can't remember which one she learns from leveling the crown, but Motet is the only one that you need). She will also need the Cure and Raise spells.
• Aire (White Mage) - She's the tough one, I found that having her White mage crown fully maxed out helps because she learns the ability "Miracle" Which fully heals and removes all status effects (Except death!) from your characters. But it's a costly 5 AP, but helps if multiple characters need healing and status effects removed. She needs to have the Healthgiver ability, Cure spell, Curaga Spell, Esuna Spell, and Arise spell.

Start of your battle by having Brandt guard and Yunita using Motet (The Boost command is the same as guarding in this game) Jusqua needs to cast Blizzard on the first cube. The most annoying thing about this boss fight is that Belphegor and all three cubes change their elemental weakness to one of the three aforementioned spells after each time you hit them with their weakness. They ALL start out weak against Blizzard. Aire needs to use Healthgiver. Now watch their moves on the next turn carefully. If the cube you hit uses Aero magic, it's weak to fire, if it uses Water/Blizzard it's weak to Aero magic, if it uses Fire, it's weak to Water Blizzard. That's the basis of this fight, you're going to have to constantly watch and pick your spells carefully. This entire fight is fought with spells only, more or less. When you start taking damage, have Brandt cast Cure, Yunita cast Cure, Jusqua attack with the opposing element, and Aire cast Cure. Your next turn should be somewhat the same, except Brandt should cast Cure again, Yunita should use boost, Jusqua attack with the opposing element, and Aire use Healthgiver.

The battle, in a nutshell: