It's important to notice that Red Cyclone's massive damage per hit and DPS do not allow for resistant units to do much at all. For this reason, even the tougher tank turns into a waste of money immediately, so it should be avoided. Instead, this stage should be beaten with cats that can target the Red Cyclone with abilities, to the point of halting his advance reliably. Cats that work well are Witch, Bishop, Pirate, Bean, Fortune Teller, Shaman, Delinquent or Apple Cat, as well as some Ubers and collab cats that affect Red and/or Floating. Cats with extra damage can be helpful to quickly kill the enemies, so they should also be used if available.
If one tackles this stage later, iCat, Apple Cat's True Form, as well as some other true forms of the aforementioned cats, can completely trivialize this stage.
Note: Most, if not, all cats should be at least level 20 and Rich Cat really helps at the beginning of the battle, but it is not required to beat the level.
All you have to do is to spam everything, starting with the cheapest cats, as the stack of Sorceress Cats that will form after a while will keep the boss under constant slowness, allowing the other attackers to quickly kill it.
Lineup: (all at least lvl 20) Mohawk, Wall, Samba (or Awa-Odori, Gold Cat etc.), Ninja, Pirate (or other anti reds/floating with freeze/slow/kb ability), Paris, Dragon. Remaining slots can be filled with strong attackers (Bahamut Cat, Whale Cat) or ubers if you have any.
Pirate is preferred but theoretically other anti reds/floating that are spamable with similar abilities would also do the job.
Start off by sending a few meatshields, this should enable you to level up your worker cat to at least 3 before pigge comes out. Shortly afterwards the Shy boys will also be spawned, and you can begin to stack your ranged attackers (paris, dragon) and spam pirate in preparation for the cyclone. At this stage, your worker cat should be about maxed and your wallet full. As your cats approach the enemy base, begin to spam all your cats and meat shields (do not worry about money as the One Horns should be easily defeated, filling the wallet). After the boss appears, it should barely be able to move due to your pirate stack. Even if it does, the extra meatshields should provide enough time for your attackers to kill it. Good luck!
Strategy 3 (no uber)
Lineup: 2-3 75c meatshields, Wall/Eraser Cat (20), Sanzo Cat, Dragon Cat (20), any anti-red tank, Valkyrie and Crazed Bahamut (20). The last slot is your choice.
At the beginning, send out your meatshields. These should tank the enemies decently. Then, upgrade as much as possible. When Shy Boy appears, send out your anti-red tank and start stacking Sanzo and Dragon Cats. When you're at Max Money, send out Crazed Bahamut Cat and Valkyrie Cat. After you do this, start spamming your meatshields and Sanzos. When the Cyclone appears, your Sanzo Cats SHOULD slow the cyclone indefinitely, making him easy. Valkyrie and Bahamut should do the rest of the work. Space Cat is now yours!