As the level suggestion says, you should be level 99 to beat it, though I beat it at level 96. Currently on my Standard Mode, I'm level 88, but I lost twice, usually on Bosses. Here's what I usually do against each Boss.
Round 5: Volcanic Lord - I usually just go with the flow, rarely use Blizzaga even if it's a bit necessary. Try avoiding those Fire patches he leaves after Firagun, and use Reflega when he casts the fire Balls.
Round 10: Yuffie+Tifa - I usually use Reflega and Knocksmash. Tifa will be easy to beat, though when Yuffie has 1 HP left, she's really annoying to beat while swifting around all the time >.< Try using Final Form for this round.
Round 15: Blizzard Lord - Since you can use summons for these set of rounds, I highly suggest you use Valor Form Genie, since Sonic does seriously high damage. With 2-3 Sonics, and a Trinity Limit, you can wipe the floor with the Blizzard Lord
Round 20: Pete - As said before, just use Valor Genie's Sonic, and Trinity Limit. Also, when Pete throws that 'Bowling Ball' at you, I usually Guard against it, and backfire it to him
Oh, and when Pete throws those small balls, go next to them, and use Reflega, and they should set it off.
Round 25: Cloud and Tifa - May be a bit hard, specially when Cloud has low HP, he gets annoying to hit. You can freely use limits for as long as you want, until your MP runs out. Just use Knocksmash, and Reflega, and you should be OK.
Round 30: Hades - Pretty easy, just use Limits, he's not that hard. Backfire his Fireballs by using Guard when it's close to you.
Round 35: Lots of Rapid Thrusters - Oh no....what ever will we do..I just go into Final Form, use Magnega and Thundaga. Master Form is also a good option.
Round 40: Cloud and Leon - This may be slightly hard, so watch out for their attacks, both together can be deadly. Since you can freely use Drive Forms, I suggest Wisdom Form, so you can stay at range. When you run out, just dive into the battle to get hit, so your Drive Gauge fills up faster. Good luck with it.
Round 45: Lots of Surveillance Bots and Armored Knights - Probably my favourite battle in the Tournament, since it's a repetition of my favorite battle in the game. The 1000 Heartless battle. Anyway, simple, just use Rising Sun, and Sparkle Beam when you get the chance. Not hard at all, consider it a break.
Round 48: Cerberus - Not so hard, just use Trinity Limit. But do try to avoid his spins and pounces. They can do some damage on you. I always go for the middle head, lock on. Like that I'd have the opportunity to get the Reaction Command, which is cool and can do some damage too.
Round 49: Cloud, Tifa, Yuffie & Leon - A very very very hard round, possibly harder than Sephiroth, if you've got low Defense. But, with my idea, I'm sure I can help you out. What I
always do is Glide around the arena, and dive in to use Reflega. You're guaranteed to get hit, so Reflega will definitely set off. Most probably it will be Leon who attacks first, so use it when he yells. Once your MP is finished, jump and Glide around the arena. You'll circle them like that, and won't stay chasing you. Thus, you have time to recharge your MP. Be careful of Leon's Fireball, with it, he can shoot you like a bird out of the sky. Hopefully you'll be fast enough to dodge it. Then just repeat the above, you should be safe, and win. Good luck again.
Round 50: Hades (again) - The final match of the Hades Paradox Cup, so you can't afford to lose. However, this time Hades can go into his immunity mode, but luckily you have Hercules by your side in this battle, giving you the opportunity to use Aura Sphere. Hades isn't that hard, but after unleashing combos on him, keep distance, since he could use that Pillar of Fire that sets him into Immunity Mode. Just use Trinity, Aura Sphere, and Reflega, and you'll win fast.
Well, that's all the bosses in the Hades Paradox Cup! Be prepared with Elixirs, and make some Boosts, just to be on the safe side.
I've done the Hades Paradox Cup hundreds of times on my main, so if you need any help, just PM me and I can help you out
Good luck with the Tournament!