This level tests your ability to spawn meatshields and keep them in front. Otherwise, your units may be swiped out by the massive HP and DMG of J.K. Bun Bun.
Spawn in Macho Cat and Wall Cat to hold back the lesser enemies that they spawn in while you save up your money. Do not attack the base for a while, as when you attack the base, J.K Bun Bun (Red/Floating) will be spawned. Once you have Max money and your wallet is as full as it can get, summon in every strong, anti-floating or anti-red cats that you have. Cats like Shaman Cat and Bahamut Cat are very helpful here. As soon as J.K Bun Bun is in battle, continue to summon every cat you have along with Macho Cat and Wall Cat. This should hold him off and kill him off when cats like Bahamut deal damage to him. Due to his health, he may be a very difficult enemy to fight and the battle may last for a long time, but it is possible.
I just use this army against J.K. Bun Bun: Samba, Wall, Monk (or Fisherman), Shaman, Swordsman, Bath, Dragon, Valkyrie, Bahamat, and Sodom. All of them had their evolved form.