Hercules is a boss who can be fought in the Hercules Cup of Olympus Coliseum in Kingdom Hearts. For this battle, Sora asks Hercules to fight him one-on-one, in a friendly competition. Although Hercules appears in Kingdom Hearts: Chain of Memories and Kingdom Hearts II, he only appears as an enemy in the first and third installments of the series, in order of release.
After defeating Hercules once during the Hercules Cup, you will gain 100 EXP from then on for defeating him.
 Kingdom Hearts
When Hercules is glowing yellow, he's invincible. Wait until he stops to admire his muscles, then pick up a barrel and toss it at him. The barrel removes the yellow glow, making him vulnerable. You do not have to wait for him to admire his muscles, but it is the time you are most likely to hit him. Make sure to throw the barrel at close-range so that you may unleash a combo of attacks on him directly afterwards. Alternatley another good method to deal damage to Hercules is to cast Stop magic, followed up by a special attack such as Ars Arcanum or Strike Raid. Use Dodge Roll to evade his punches, and jump to safety when he punches the ground to regain his glow.
When Hercules is back on his feet, watch out for his counterattacks. Note that almost all the time, when he is made vulnerable by a barrel, he counters with a punch. Evade it, and then hit him! Occasionally, when you throw a barrel at him, he will be stunned. Use that to your advantage and land a few blows on him. Use Glide to float around and dodge his charging attack, or use Guard to stop him and leave him vulnerable. Periodically, Hercules will do a spinning tornado attack, which destroys all barrels on the field, which will reappear seconds later. After Hercules finishes his attack, he'll get dizzy and if he isn't glowing, he's open for you to attack him.
If he isn't glowing when he uses these attacks, you can stop him by counterattacking, however, it would probably be wiser to wait for him to admire his muscles, and then repeat the strategy all over again.
 Kingdom Hearts II
Hercules does almost the same moves from Kingdom Hearts (except for the spinning tornado attack), and this time there is no yellow glow around his body, making him open to attacks. The only time a yellow glow is seen is when he is about to charge up for a powerful punch.
Evade the attacks he makes—use Dodge Roll and Glide to the best of your ability, and do not be shy about using physical attacks. Any kind of Reflect magic you have works very well for almost every attack he does. It is also possible to block an attack with Guard, then use Counterguard if you have it.
Hercules is unarguably a much easier opponent than in Kingdom Hearts, and constant attacking should enable you to take down Hercules.