Overdrive definitely does make a difference, never attempt to go against a boss without it. You can make sure you do this by using Yuna's Great Summons which gives automatic full o.d.

My other advice is train Yojimbo by going against lesser arena monsters and making sure he does waki or zanmato to improve yr relationship with him. Repeat until u r tired of it, and SAVE. Then try again against a boss. NEVER EVER DONT PAY HIM OR SEND HIM AWAY OR LET HIM LOSE. Reset if this happens.

Hopefully if you are making progress u should be able to pay him less than 100,000 gil. I ended up paying him only 5000 but I do have the PAL version.