Dawn of Gaia is the fourth stage in Parthenon.
From the start, keep spawning Major Space Cat. If you are lucky, Major Space cat will trigger a critical and you can proceed. If he doesn't you can quit and get back your energy. By repeating this hundreds of times, you are bound to get lucky.
Miss Moneko also had good chance of Critical hit (15%) and higher damage than Space Cat, give her a try. You can get her easier than Space Cat by the way.
The hardest enemy of this level would be the Metal One Horn, so bringing along anti-metal cats, such as Bronze Cat, is greatly advised. Otherwise, bring units with high health and/or quick attack speeds. Also make sure to bring along units that can score critical attacks, such as Island Cat, Major Space Cat, Miss Moneko, Crazed Fish Cat, etc.
If you have the Marauder Cat or its evolved form, Berserker Cat, this level can be completed easily as long as he is shielded.