The Unicycle Cats may be strong, but their time between attacks is all backswing, making it possible to sync all of them using the default Cat Cannon and greatly reduce their ability to push; and while they do outrange Gross Cat and Paris Cat, they still can't reach Crazed Bahamut Cat, Ururun Cat or most Uber Rare Cats.
Lineup: Any 5 meatshields that cost less than 150¢, Crazed Bahamut Cat. Use a Cat CPU.
Start: Let the peons or starting enemies attack your base until your Worker Cat is maxed and your wallet is full, now spawn all meatshields and Bahamut.
After attacking base: Unicycle Cats appear. Continue spawning meatshields. Let them stack first and fire the Cat Cannon, turn on the Cat CPU, and watch. (Make sure that if Bahamut attacks them, they are still stacked.)
NOTE: There may be a chance to let Bahamut knock them back to the base and have Bahamut just wreck the base. Easy win.
Strategy 2 (ft. Kubilan Pasalan)
Stall the peons for a short while to upgrade the Worker Cat and fill your wallet. Then, spawn Bahamut and Kubilan Pasalan and send in the meatshields. When all of the Unicycle Cats appear, use the Cat Cannon to synchronize their attacks. This will make them deal less damage. Spawn everything you have, and stop spawning the anti-reds when One Horn is defeated. Kubilan will push all the enemies back if well protected, and you should be able to defeat this level without needing to kill the main bosses.