Begin the battle, increase money capacity level, spam Crazed Wall Cat and Wall Cat to block the Doge Darks and use (few number of) The Flying Cat to knock the dogs back. When the money is full, spawn all cat units player equipped.
Raise money first by deploying meat shields and rangers like Salon Cats. You may stack up Bahamut Cat if you want but I recommend you to stack up Hip Hop cats. The biggest threat is the Shy Boy but the Hip Hop cats can freeze it for a while.