Using many anti-Red and anti-Floating cats can make this stage easier than you'd think. After the Shy boys and St. Pigge is spawned, a lot of money could be accumulated to level up your wallet/spam cats. With the assistance of anti-red/floating cats, Attack on R-Cyclone can quickly be turned into the easiest cyclone stage.
Line-up 1 (ft. The red busters)
If you have Momotaro, spam him in his unevolved form with a few meatshields. Since he has a 30% chance to freeze Red enemies. all the enemies will be frozen forever.
Line-up 2 (Classic strategy)
Wall Cat, Brah Cats, Sorceress Cat, Necromancer Cat, Sword Master Cat, Drama Cats, Dragon Cat, True Valkyrie Cat and Bahamut Cat (most, if not, all cats should be at least level 20 and Rich Cat really helps in the beginning of the battle, but it is not required to beat the level)
The One Horns fill up your wallet, making this the easiest Cyclone stage.
Another reason why this stage could be so easy is because of the humongous amount of anti-red + anti-floating cats.
Line-up 3 (ft. Thundia)
It is recommended to bring along Rich Cat and Sniper the Cat.
Start by spamming Wall Cat. You will be doing this throughout the battle.
Once the B.B.Bunnys start coming out, spam Wall Cat and Ninja Frog Cat. To efficiently do this, while also gaining money, use a pattern like this: Wall/Ninja Frog/Wall/Repeat. This will allow you to build up money, albeit slower than just Wall Cats.
Once you've gained enough money, spawn Thundia.
When the Shy Boys spawn, spam everything you have (except Angry Delinquent, Whale, Thundia) to slow them down long enough to allow Thundia to defeat them.
Once the Cyclone comes out, spam everything. Do not turn off Sniper the Cat at any point. If you send out enough Pirate Cats and other knockback or freezing units, the Cyclone should barely be able to move for a good time.
Once the Cyclone is down, destroy the enemy base and you will win!
The One Horns will, as stated above, provide extra money, allowing you to continue spamming.
Line-up 4 (ft. Pirate swarming)
You can add Sniper the Cat, too.
There's no real strategy for this, as the Pirate stack will do the job. Stack enough of them and Red Cyclone will be completely stunlocked and will be able to barely move. Though, I don't think this will always work, as it's up to RNG. Having Pirate Cat's True Form should almost guarantee that this works.
Line-up 5 (ft. one of the worst Ubers ever: Wargod Masamune)
Basically, the strategy is to lure the Shy Boys to your base, summon your Ubers, and cat-spam. Your goal is to keep the Red Cyclone at the enemy base by using your 3 freezers and your knockbacker. The reason I didn't use Brah Cats is that they have too little range, and not as much attack. I recommend that if the cats listed have a True Form that has either the same or higher range, use it. This strategy mostly relies on RNG, so it won't always work. Max out all the cats used before attempting this stage.
A simple summary would be this: Knock back the Cyclone and freeze it so it cannot attack. Then finish it off with Ubers and Crazed Bahamut. Good luck!
Line-up 6 (ft. Elemental Duelist Cat)
Start stalling by spamming Erasers and E. Duelists. Upgrade the Worker Cat while doing so. Once the Shy Boys come out, spam the cats in your front row and the first three of the back row. The Shy Boys should soon perish and your money will fill up. At that point, spam everything you have. Even after the Red Cyclone comes out, just keep spamming. You need 300% Relativity Clock Treasures to use a second Bahamut. In my experience, R-Cyclone cut through my Bahamut and Dioramos and cut throughout the rest of my spam until it almost reached the base, and then a hit from Bahamut dealt him the finishing blow.
Strategy 7 (ft. Necromancer & Monk Cat/Great for mid-game)
Similar to strategy 4, it's basically just a stunlock team containing Necromancer and Angry Delinquent and a string of good RNG to keep it stunlocked. Just have your mid-game damage units (Paris, Macho Leg, Dragon) just tear into it. The upside of this compared line-up 4 is that Bahamut won't miss (I think if the Cyclone is knocked back even for 0 distance attacks still miss also that his collision and detection gets removed causing all your cats to walk into certain death with his very respectable dps). Red Cyclone really is just a snowball capitalising when all your utilities are dead and at that point there is no coming back so it's a go big or go home situation but in my attempt I had it frozen 98% of his time in existence (with the other 2% being it slowed which means by capitalising on his miniscule attack range he can't attack)
Line-up 8 (Anti-red/meat shield spam)
Lineup: (all at least lvl 20) Mohawk, Wall, Samba, Ninja, Pirate (or other anti reds/floating with freeze/slow/kb ability), Paris, Dragon, Whale (or other anti-red/floating). Remaining slots can be filled with strong attackers (Bahamut Cat) or ubers if you have any.
This is mostly a combination of two different strategies, (1 and 4). 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 meat shields, this should be enable you to lvl 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 near the enemy's base, begin to spam all your cats and meat shields. (Do not worry about money as the horns should be easily defeated, providing extra money). After the boss appears, it should barely be able to move due to your pirate stack. Even if it does the extra meat shields should provide enough time for your attackers to kill it. Good luck!