NOTE: You can fight both Geryon and Proto-Babil as many times as you want.

He is an entity reformed by the 4-archfiends aura and wield all the archfields' attacks. he can be found in the second and third playthroughs in 2 locations after defeated the 4 archfiends.

Is where you defeated the 4 archfiends. Talk to the square tile in the middle. You're probably not able to defeat him here if you don't have equipment that immune to Curse, so move on and wait to defeat him at Mount Ordeals instead.

Is on top of the Mount Ordeals where Cecil became Paladin.

There is not much of a strategy here as long as you have equipment that prevent Curse then he is a piece of cake. Here are equipment that prevent Curse: Ribbon, Crystal Shield, Onion Shield, Adamant Armor.

Yes, it's possible to use auto-battle attack against Geryon but you'll need to max out stats and a specific equipment to do so, 5 Adamant Armors and 5 Cursed Rings.

Cursed Ring can be farmed from Soul and Spirit at Mount Ordeals. Use Siren at the entrance to encounter them. The drop rate is quite high, I got 5 rings in 5~10 minutes.

I highly recommend you max out stats and have at least 6000 HP before you want to try your luck. He is so powerful that can KO your entire party in a single hit with Laser Barrage or Divine Judgement. Another power attack is Light of Babil which deals 9999 damage to a single ally.

He is on the Lunar Surface. Fly to the north, slightly east, you'll see a rock shaped like a human face. Talk to it, a dialog appears then select Dark Matter to fight him.

Preparation:

• Equip Draw Attacks, Brace, and Phoenix on Kain (or anyone you like) to serve as a tank. 
• Cecil with Love, Darkness, Focus, and Limit Break.
• Rosa with Dualcast, Omnicast, and Fast Talker.
• Rydia with Dualcast, Cry, and Fast Talker.
• Edge with Throw, Bless, Steal, and Phoenix.

During the battle: 

• Kain immediately use Brace; normally Light of Babil deal 9999 damage regardless Adamant Armor, with Brace, the damage reduces 2500. 
• Rosa casts Slow, Haste, and Shell. After that, keep her standby waiting to heal the party.
• Cecil Focus 2 times, enter Darkness mode, then attack with Love augment (between 70,000 to 99,999 damage). Repeat 2-Focus and Attack until Darkness effect wore off, that when you need to use Darkness again.
• Rydia uses Cry once, then casts Flare twice (or Meteor, your choice); she deals around 6000 with Flare.
• Edge uses Bless and Steal Megalixir. After that, he can attack/throw or heal any ally with Elixir.

There are some circumstances when Proto-Babil keeps spamming Laser Barrage and Divine Judgement. You cannot do anything at this point, that's when the Phoenix helps you survive the annihilation.