What you need for this cup is strategy. Abuse the privileages you have. The first 10 rounds are pretty easy, but with the Tifa and Yuffie battle I just used Wisdom Form to kill Tifa pretty quickly then just slowly killed Yuffie.
In the next 10 rounds with the Titan Cup style fighting, I just use summons a lot (mostly Genie because he does the most damage) and used magnega to get all the enemies in one place. With Pete just use lots of summons and try to get him in the air a lot. And make sure that you are constantly using summons, and try not to get hit so much.
In the next 10 rounds with the Pain and Panic style fighting, I just use Donald's Comet a lot (don't worry, it only takes up like 10 mp, so you can use it over and over) and again use magnega.
In the next 10 rounds with the Cerberus Cup, style fighting, I just used Wisdom Form (with the Sorcerors especially) and Final Form a lot.
I might finish it later. In short, use what you have, cast magnega a lot, and use strategies that you used in the past cups to your advantage.