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.
Strategy 1 (up to 4-star)
Lineup: Skelecat, Mr, Necromancer, Butterfly Cat, Wrestling Cat (32), Awakened Bahamut Cat (30), Li'l Lion Cat (33), Ramen Cat (40+7), Catellite (40+7), last slot is of your choice.
Combos: Double Research Combo, Sportswoman (Unit Defense UP Sm).
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.
Lineup: 3-4 75c meatshields, Thaumaturge Cat (optional), Macho Legs Cat, Cat Eastwood, Dragon Cat, True Valkyrie, Crazed Bahamut and a long-ranged tanky uber or 2 if you have any.
IMPORTANT!! Do NOT bring wall cat variants or, if there is no other option, bring them in their first form.
When the Doge Darks appear, start spamming meatshields and Thaumaturges and continuously upgrade. If the Doge Darks get too close to your base, send out Macho Legs and/or Dragon to knock them back. when you are at max money, send out Valkyrie and Bahamut. Don't spam anymore and start feathering instead. When Bun Bun Black appears, start feathering slightly faster. This will prevent Kory from making too many Shockwaves, as the shockwave will only appear if a cat is in the range of the enemy (not including the shockwave). Bun Bun will keep killing the meatshields, meaning Kory won't make too many shockwaves.