The trick in defeating the Minotaur is to first destroying his armor before finally killing him.

In summary, to do this, the first time around you will have to damage him. It takes approximately 13 hits to start making holes in his armor (it will take more hits later on though). When you've done enough damage to him, you'll have the "mini-action" sequence where the Minotaur will cower near the gate and you can major damage by pressing the appointed buttons.

O.K. Now for the specifics.

The first thing you have to do is damage the Minotaur without taking damage yourself. This is possible. You'll notice that fighting directly on the ground floor will either get yourself incinerated or slammed as a new floor ornament by the Minotaurs' hooves and horns. This also applies for direct combat on the second floor where the Minotaur has the bad habit using flying molten lava/ liquid metal against you.

There is however, a safe spot. This on the right side of the screen, on the stairs behind the Minotaurs' (to your right) hoof. Use your long-ranged Chaos blades and attack appropriately. The Minotaur will attack 2 separate different attacks. The first is a single frontal attack. Remember to block when the hoof comes back to its original position. The second attack is more dangerous. It's a 2-combo sweep attack, so remember to keep blocking after you've blocked the first part of the combo sweep. You will not lose any life while blocking these attack. If you are not close enough to the hoof, the Minotaur will retreat to the area near the gate so you have to step forward a little to provoke the Minotaur in the frontal stance.

After the sufficient damage, the Minotaur will cower into Defence mode, where you have the chance to go into "mini game sequence". Press the appropriate buttons to successfully attack the Minotaur. You will notice that after a successful attack, the Minotaur will be stunned. Normally, this is the perfect chance to use "Burning Log sling-shot". But refrain from doing this. Why? Because its faster using the Hermes superhuman skill to damage the Minotaur on each stage of damaging his armor. Each of the "mini-game sequence" will charge the Hermes skill half gauge. So before activating the sling shot, make sure your Hermes gauge is full first (this is optional of course, but much faster than manually attacking him). Oh, make sure your near or en route to the Minotaur before he goes into Defence mode or you'll miss the chance to attack him.

Repeat this process until the armor breaks and continue attacking him until the last "mini-game sequence" attack to finally finish him off. You can use your access magic points to further hasten the damage by using Poisedon's skill.