This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
It's easier than it looks. Don't attack the center, but instead focus
your attacks on the flames. One of the flames holds the Son's HP - if
you hit it, the Son of Sun will lose HP. The other flames just
Find that one flame through trial and error, then rank on it up until
the Son of Sun shuffles the flames. Then, find it again and repeat the
process until the Son of Sun becomes the Moon Stone.
Alternatively, if you have the secret character in your party, have the
secret character cast "Black Hole". Some of the Son of Sun's flames will
be swept away, so your chances of finding the real flame is much higher.
This works until the Son of Sun uses Roulette to shuffle the flames, and
then the other flames will be back.