Ah, yes, the Criosphynx. The "crazy moon language" he's speaking is Latin, and you have to solve his riddles to beat him. Defeating him this way, however, gives you no reward other than the order in which the Chrono Cross must be played.

"Auburn nay the burn, Iron pyrite nay the fool, All that glitters is
nay...But silence be..."
Iron Pyrite=Fool's Gold=Yellow

"In my anger, I see...Both the rag to charge at, and the flag to stop at.
Blushing, I walk the royal carpet."
Anger=red, red light=stop, red carpet=royal

"It isn't easy being...A friend of the planet, With the jealous monster's
eyes giving me a sign to proceed."
Jealous="Green with envy"

"Mare et caelum et viola, Give me a melancholy gloom, But a first prize
ribbon, Makes me feel I've royal blood!"
Latin translation say that "The sea and the sky are this" and also a blue first place ribbon or the blue bloods.

"Like pontoon nay the knave, Or Jolly Roger nay the bones, Even the top rank of self-defense, be no protection from the plague."
Black

"What the extorted one is bled, With knuckles of fear. The plumage of a
coward when faced with the hottest of heat."
White Fire is the hottest fire. Turning tail and running away.

Alternatively to beating him by solving his riddles, you can just beat the crap out of him. Use your strongest character equipped with a Yellow Plate and he'll be dead in about 10 minutes. Don't worry about reviving your other characters, they are gonna die anyway.