After that, Li'l Bun Buns will come out. Buy your strongest and fastest cats, protecting them with meatshields.
When you beat the Li'l Bun Buns, Zackie Pengs will come out. Spam your meatshields and your strong cats again. Zackie Pengs attack very fast and deal much more damage than many other enemies so spam your Cow Cats / Giraffe Cats to help manage them. They will die quickly and/or protect them with your meatshields.
When another Li'l Bun Bun comes, spam your meatshields until you have saved enough money to buy a strong cat like Bahamut Cat etc. Use this to attack Li'l Bun Bun, with protection from your meatshields or Li'l Bun Bun will destroy your meatshields and defeat your base.
After that, the Face isn't much of a problem, so the hard part is over. Onward to victory!