In the beginning, use only Wall Cats to block the peons from your base. Upgrade your Worker Cat to Level 4, but use Paris Cats to kill enemies if they start to push through your Wall Cats.
Once your Worker Cat is at Level 4, you can either:
A: Continue to upgrade Worker Cat to Level 8 and wait for maximum money, or...
B: Start sending out Wall Cats, Paris Cats, Dragon Cats, and the Anti-Metal Cats.
When your Cats hit the half-way point, start sending out Macho Cats to accompany them. The Lollycat will appear when the enemy base hits the 495,000 mark.
The Lollycat doesn't hit as hard as most other Awakened Enemies, but it attacks fast with a long range. Keep sending out meatshields to prevent them from pushing, and use Paris Cats for damage. The real threats are the Metal Hippoes (if you don't have an Anti-Metal Cat), the Heavenly Hippoes, and the Gabriels.
If you're getting extra money from killing the enemies, save up for Valkyrie Cat, but do not stop sending out Macho and Wall Cats.
Continue this process, and remember the Lollycat gets knocked back 4 times. Use the Cat Cannon whenever it is ready.