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.
The key to fighting Apollo is to jump on him immediately and keep
fighting. When you first find him, he won't attack you for at least six
or so rounds, so fight now.
This may sound self-explanatory, but use your best weapons against him.
The Samurai Bow seems to be quite effective, and so is the Excalibur.
If a character should become stunned, make sure one of your stronger
characters has the Heart MAGI equipped so he/she/it can revive fallen
When Apollo's HP becomes critical, he'll start melting. Apollo will
explode when his HP reaches 0.
NOTE: In order to win this battle, Dad and at least one other character
must still be alive when Apollo starts melting. If not, Apollo will
explode and destroy your party almost instantly.