This red variant of Kory is almost the same, performing a medium attack and firing a Shockwave. However, the shockwave range has been tripled, making him very hard to defeat. He also loses most of his knock-backs, causing more shockwaves if you don't have any anti-red cats.
One day I woke from a nap to find a Kory making stew in my kitchen. After I kicked him out for raiding my fridge, it seems the sunset on his back awoke his hidden dark powers.
Ubers like Kamukura, Raiden, Mighty Lord Gao, and Cat Machine can also help. Kamukura and Raiden can use their special abilities to slow down Berserkory, while Cat Machine can soak up many hits and damage Berserkory for quite a while (True Form is even better against him because he can protect units behind him thanks to his special ability). Mighty Lord Gao is immune to shockwaves, can critical attack with an area attack, and is strong against any enemy with a trait. Dread Pirate Catley is also extremely helpful in knocking him back.
A great way to defeat Berserkory is to use Wrestling Cat, Maiden Cat's true form. Against red enemies, she has about 90,000 effective health, even more when above 30 with Catseyes. Because of this, she can stall the demonic koala and damage him for quite a bit of health.
Fried Shrimp Cats can also sponge a ton of hits, about 120,000 damage, and also weaken Berserkory. They also do a good bit of damage as well.
Berserkory has lower range than Kory does, so a stack of ranged attackers can be quite effective.
If you have iCat (True form of Apple Cat), then place 2 of them precisely. Doing so, this will render Beserkory powerless (granted there aren't any other main attackers for support), which you can then finish off easily.