The 'ultimate battle' is probably Champion Diantha. That's probably the strongest trainer in the game, aside a few others and actual legendary Pokemon themselves.
There are spoilers below btw but I doubt you care I just felt it was necessary.
I can recall a very tough battle that you encounter during the Looker missions. In Chapter 4, you have to battle Emma's robot and her high-leveled Pokemon, I remember that being a very tough battle. Although it's not really 'The Ultimate Battle', it's a pretty tough battle.
Hope I helped. :)