Bring some meatshields, and stall at first until you get 3 Bahamut Cats. This will greatly increase your chances of winning.
Also, this level might also drop a Treasure Radar!
If you are doing this stage in 2 or 3 stars, I highly recommend that you bring some health chipping/tanky cats and crazed bahamut. Lineup: Crazed/Manic Macho, Macho/Mohawk, Gato Amigo/Samba Cat, Crazed Wall (Level 20 is a requirement) Thaumaturge, Crazed UFO (Level 20 highly recommended), Crazed Dragon (Level 10-20), (Crazed M. Titan Level 20 Required), Crazed Bahamut (Level 30), and either King Dragon, or a high damage dealing uber, like Lufalan Pasalan. When you start the battle, be sure to stall until you get a max worker cat with maxed money, and make sure to stack your dual dragons (if you don't have a high damage dealing uber). Thaumaturge is for weakening the Otta Smack-Us, Duches, and R.Ost (if the R.Ost is alone) so they don't push through your front line. Crazed Dragon/King Dragon and UFO are mainly for chipping small amounts of health of the R.Ost, and killing the extremely irritating peons. Crazed M. Titan is mainly your tanky unit to stall the peons in the beginning so you can max your worker cat. Also, if you don't have Crazed Dragon, you can replace Cyborg for him. Lastly, a level 20 Crazed Wall can tank about 3-4 hits from the R.Ost (if it isn't weakened) and about 5-6 hits (if it is weakened). Hope this strategy works!
My method of beating this was fairly generic, but doesn't severely rely on luck.
Loadoat: 5 Meatshields(could probably do with 4) ( I used Macho cat, Eraser, Gata Amigo(Samba works too), catburger, and Jiangshi, all level 30+ except for macho, which is 20+9) Magica cat, (level 28+2), Cyborg(paris works too, 30+1), Dragon,(20+7) Greater Demon Cat(30) and Crazed Bahamut(30).
Greater Demon Cat can likely be subbed out for any high damage uber, and if you have no ubers, just go with dual dragons. It's the cyborg/Paris that really matters.
Start off with a few erasers and no more than 3-4 Cyborgs. Once Duchies are dead, stall whatever peons come, until you have about 8k. Then send out bahamut and Greater Demon, as well as consistently spamming meatshields, Dragons, and Cyborgs. Magica cat is only useful for weakening the R.Ost so that Greater Demon can hit it.
TL;DR stall for cash, send bahamut, spam everything.
Strategy 3 (4-star):
This worked for me fairly easily.
Row 1: Li'l Mohawk (Level 50), Gato Amigo (40), Li'l Eraser (53), Jiangshi (49), Ramen (53). Row 2: Thaumaturge (44), Vendor Cat and Kitten (33) [probably optional, maybe replace with Pastry Cat?], Cyborg (51), Dark Emperor Catdam (29), Awakened Bahamut (30)
Battle Items: Speed up (optional), Cat CPU (semi-optional, depends on how much abuse your fingers can take.)
Level up your wallet twice as the critters approach, then begin spamming Jiangshi and Ramen. When Otta-smack-u joins the mix, start spamming everything in row 1, tossing in the occasional Thaumaturge and Cyborg and leveling up your wallet when you can. Take care to slow down summoning your cats if you're approaching the enemy base. You'll want to make sure that you've filled your wallet before you hit the base and summon R. Ost. Once you fill that wallet to max, go ahead and summon Catdam. Once R. Ost appears, bring out A. Bahamut. Then, either start spamming everything or hit Cat CPU. Then you win, then you get to eat mice or whatever.