How did I miss this?

[CptOvaltine]

So I've been playing Chrono Cross about once every year or two since it came out, and I've never heard of the Criosphinx until today! 

What is this monster, and how do I fight it?!

[Acacia Sgt]

The Criosphinx is more or less a bonus boss, found in Another Earth Dragon isle, where you fought the Earth Dragon in the other dimension.

Its fight basically goes like the Time Devourer's. You can more or less fight it out, or cast elements of the appropiate color. Which color is told by the Criosphynx itself, in riddle. Shouldn't be hard to figure it out, though I'm sure you can just look up the order. I don't think it's random, though I just don't remember if so.

[Boo the Gentleman Caller]

And you get an awesome accessory out of it! It's worth completing this sidequest!

[CptOvaltine]

At what point in the game do you trigger the side quest?

[Acacia Sgt]

I believe it's at least after fighting the Earth Dragon in Home World. The island in Another world doesn't have the path open until you do it's Anotehr World counterpart first. That should be the only requirement, I think.