There will spawn only one Unicycle Cat, so don't be too alarmed. Because of that, this might be considered the easiest awakened stage of all.
A good way to beat this stage is to spam meatshields (Cat, Tank Cat, etc.) and spawn a high leveled Bahamut Cat (at least 15 or above) and keep spaming until the Unicycle Cat is beaten. If you have any ubers or other high-damage cats, including True Valkyrie cat, use them as well. Congratulations! You have beaten this stage. You can now spam any cat. Don't try the second stage as it is not necessary. Just use a treasure radar the first time: it is worth it