A few very weak peons will spawn to distract you. Once the base is damaged, Teacher Bun Bun (Floating) will spawn followed by J.K Bun Bun (Red/Floating) and then Bun Bun Black(Black/Floating) and lastly Bun Bun Symbiote (Alien/Floating). Peons will constantly spawn throughout the game.
Lineup: Crazed Macho/Manic Mohawk Cat, Eraser Cat, Crazed Wall/Manic Eraser Cat, Jiangshi Cat, Sanzo Cat, Cameraman Cat, Tathagata Cat / Octopus Cat, Holy Valkyrie Cat, Bahamut Cat/Crazed Bahamut, and Ururun Wolf.
At the beginning of the level, let the peons hit your base, and upgrade the Worker Cat until it's level 8 and you have maximum money. From there, spam your first 3 meatshields, Sanzo Cat, Cameraman Cat, and Tathagata Cat, and spawn Holy Valkyrie Cat.
When the base is hit, Teacher Bun Bun will appear, but he should be no match for the endless slowing effect of Sanzo Cat and the high anti-Floating damage of Cameraman Cat. When J.K. Bun Bun comes out, start spamming Jiangshi Cat in addition to your other meatshields. You should also send Bahamut and Ururun Wolf at this time if you have enough money. Bun Bun Black isn't much of a threat here, so there's not much to say about him.
The scariest part of the level is the Bun Bun Symbiote. One shockwave will total your entire stack of Sanzo and Cameraman Cats, not to mention all your heavy hitters. Tathagata Cat's weaken effect comes in handy here, and Octopus Cat's wave blocker effect will negate the threat entirely (as well as tanking Bun Bun hits for some time).
Once all the Teacher Bun Buns die, you are free to win the level
Strategy 2 (Cheese)
If you have Li'l Tank Cat/Li'l Wall Cat, this level can be easily won without having to fight the Bun Buns at all. Simply send a couple of Li'l Tanks out at the beginning and wait for them to reach the enemy base and begin damaging it. (You may want to fire the Cat Cannon to clear out enemy peons to make the first part faster.) They will damage the base so slowly that peons will back up behind the base until the enemy limit is reached so that Teacher Bun Bun and the others will be unable to spawn. After enough enemies are stacked up behind the base, simply begin spamming Li'l Tank and/or Li'l Cat to slowly wear the enemy base down. To speed it up, you may also want to send Maglev Cat and Awakened Bahamut once all the peons are behind the base.
Bringing any attacker without LD/waves will greatly help once the enemy limit is reached.