Sphinx

Sphinx is the name of the monster who is the boss of the pyramids. She is an unwinnable fight. However, getting her HP to 0 unlocks the Ancient Law of Ecstasy attack, which is required for an achievement.

Normal difficulty
Premise: Guard when Sphinx is about to attack with her Kiss of Death.

Turn 1: Summon Sylph.

Turn 2-3: Attack.

Turn 4: Use Death Sword Chaos Star.

Turn 5-8: Attack.

Turn 9: If your HP are above 150 use Death Sword Chaos Star, otherwise use Meditation.

Turn 10+: If you used Death Sword Chaos Star, then build enough SP to kill Sphinx with your next skill, otherwise build enough to summon Sylph and do so.

Keep attacking/guarding/healing as necessary.

Hard difficulty
Premise: Guard when Sphinx is about to attack with her Kiss of Death.

Turn 1: Use Thunder Thrust.

Turn 2: Summon Sylph.

Turn 3-6: Attack.

Turn 7: If your HP are above 170 use Death Sword Chaos Star, otherwise use Meditation.

Turn 8-9: Attack.

Turn 10: If your HP are above 95 summon Sylph, otherwise use Meditation (attack to build SP if necessary) and summon Sylph as soon as possible.

Turn 11: Attack until you have 4SP.

Turn 14/15: If your HP are above 170 or if Sphinx would die from it use Death Sword Chaos Star, otherwise use Meditation.

Turn 15/16: Attack until you have 4SP.

Turn 18: If your HP are above 60 or if Sphinx would die from it use Death Sword Chaos Star, otherwise use Meditation.

Keep attacking and using attack techniques as you see fit until you win.

Hell difficulty
Her Kiss of Death is nearly unavoidable and used frequently, making her unbeatable.