My easiest battle was probably Bertha, the Ground-type user in the Elite Four. I had a Torterra and a Golduck that already would've beat her to a pulp, but the one advantage she had against me (I had a Fire type), was also part Fighting. It wasn't that hard at all. The only hard part I faced was that Hippowdon, who's health was incredibly high.
The hardest, I would have to say was Palmer. I've never beaten him. His team(s) in the Battle Tower are near impossible to beat. If you've sucessfully managed to beat all 49 levels on the Battle Tower I give you a large round of applause.
Cynthia was kinda hard too, but I beat her Garchomp easily with my own Garchomp, and the others were easy. The only one who I hated was Milotic, who my Grass/Ground type couldn't kill since it knew Ice Beam, and I had no Electric types. Eventually I just taught my Alakazam Charge Beam and won. Woopee.