What you can do:
Fight in a duell made of 8 battles. When you have won all 8, you will reccive BP (BattlePoints) and then you can Exhange the BP for items. When you have gotten the three most expensive prizes, you can fight in a special duell, where the last opponent is Proud Clad.

Special Items:

OmniSlash - Cloud`s forth limit break

W-Summon - Abillity to summon a monster two times per round, or two monsters in the same round, with one character!

Final Attack - Gives you one final attack when you dies. Pair it with another materia to use that materia when you die.
(Reccived in special battle.)

Champions Belt - Very good armor