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Be at level 80 or higher. Equip yourself with items that boost your defense or your health. If you haven't already, get the Ultima Weapon. Enter the tournament.
That way, if you don't have the ultima weapon yet, you'll still have decent magic and attack power. For example, the Second Chance and Once More abilities. Ensure that all of your items slots are equipped with elixirs. This will greatly increase your attack power by 12 and your MP by 2. Either way, it's an incredible and invaluable upgrade. Follow the rest of the guide in Method 1 above for the combat phase. However, be even more mindful of when Sephiroth begins running in circles. If you're not at a high level, you'll have trouble ending this phase quickly, so make sure you're absolutely ready by the time you start.