Labyrinth of Hades (ハデスの迷宮) is the last stage in Parthenon.
Kory appears as a major threat to your cats.
Bun Bun Black appears as a boss.
Spam meatshields and long-range wave attackers such as Crazed Sexy Legs Cat.
The Kory is a major threat. Basically, if it was only Kory you could just spam long-rangers. However, if you do that, Bun Bun Black will just kill them quickly. So you will need to use meatshields, 2 is recommended. The rest should be filled with long rangers such as Paris Cat.
Don't bring any units if their Health/Knockback is lower than 2800 (5600 for a close ranger) because 2800 is the damage of Kory's waves.
Bring at least one anti-floating/anti-black character for Bun Bun Black, though not knockback, slow, or freeze. While they can stall Bun Bun Black for a few moments, Kory will be able to shockwave much more easily.
Once Bun Bun Black is knocked back, this is a golden opportunity for you to attack Kory (he's knocked back once every 77,777 health).
You can avoid Kory's shockwaves by using weak meatshields so that when they're killed by Bun Bun Black, Kory will miss, and the attack wave won't form. For example, the true form of Tank Cat, Eraser Cat withstands a Bun Bun Black hit, being victim to Kory's waves, while his evolved form will die from Bun Bun Black's attacks, making Kory miss his target.
In any case, you'll need meatshields to protect your units from the Bun Bun Black.
If you have Octopus Cat, you pretty much win as long as you shield him from the Doge Darks. He has high health so he can take various hits from Kory while also blocking his waves and saving your backline, takes 1/4 damage from floating (1/5 with treasures, which could become a whopping 1/10 if he weakens Bun Bun Black), effectively stalling Bun Bun Black. With Octo, all you need is to send constant meatshielding, ensure you have money to keep respawning Octopuses, and stack attackers.
For 4 star difficulty, this can be quite difficult as Bun-Bun and Kory will pretty much destroy your units with the 3.0 magnification. It is suggested to use the double research combo (Skelecat, Mr., Necromancer), along with Cameramen + Paris Stacking. Also, you could stack Necro-dancers along with Cameramen, and do perfect timing with A. Bahamut to kill Kory and Bun-Bun. Awakened Bahamut should be deployed just right before they sync in position.
4-Star Strategy 2.0
Line-up: *Skelecat, *Mr., *Necromancer, **Butterfly Cat (or fishman doesn't matter), **Wrestling Cat (32), Awakened Bahamut Cat (30), Li'l Lion Cat (33), Ramen Cat (40+7), Catellite (40+7)
*Double Research Combo
**Sportswoman (Unit Defense UP Sm)
Note: You may notice that there is a blank slot. Feel free to fill this slot with any cat you wish to bring. I would have also brought Li'l Jamiera Cat, but mine wasn't strong enough (lvl 35) to be able to land a hit before dying. I brought Robocat as he helps a bit once Kory dies. He was useless before then though because he would always get knocked back by Kory's waves.
Note 2: If you have the Bad Guys combo (Research Power UP L; composed of Lasvoss, Li'l Nyandam, and Killer Cat), use that instead of the Double Research Combo. Although it is very possible with Double Research, Bad Guys makes things easier.
Stall at the beginning with Catellite and Ramen. Upgrade your Wallet to max while doing so as well. Once your Wallet is full, start spamming Wrestling, Ramen, and Catellite and spawn Li'l Lion Cat only every now and then (I just make sure that there are at most 4 Li'l Lions on the field). Once Kory and Bun Bun spawn, send Bahamut. He will definitely die quickly if you don't time it right, but that's okay. This strategy is for those like me who don't time such things. Just make sure to use the Cat Cannon as often as possible, keep sending the four other cats like before, and spawn Bahamut whenever you can. Kory will die first, and Bun Bun should be easy enough to beat. You win!
4-Star Strategy 2.1 (A theoretical variation on 4-Star Strategy 2.0)
With a high leveled Li'l Lion and/or Wrestling Cat, it may be possible to just wait for the enemies after the shockwave to get close to your base and stall from there. With the stated levels in Strategy 2.0, I was able to stall for only a pretty short time, but I can imagine it working.