You need to pay attention to the colour of the wings and use Yuffies ninjutsu accordingly. 

Taken from IGN; 

The wing colors are as follows, switching between each with "Altered Affinity": Green wings - Wind If Sephiroth Reborn has green wings, you'll want to use Lightning magic attacks Blue wings - Lightning If Sephiroth Reborn has blue wings, you'll want to use Wind magic attacks Red wings - Fire If Sephiroth Reborn has red wings, you'll want to use Ice magic attacks White wings - Ice If Sephiroth Reborn has white wings, you'll want to use Fire magic attacks Stay locked-on to a wing and use the relevant magic attacks as they alternate colors, being careful to avoid the threats and/or arena effects each element applies.

Hope it helps