For Aaron with his bugs, use Infernape for fire. For Beautifly and Vespiquen, use a rock move (they're double-weak). Heracross is double-weak to Flying, and Drapion is just a pain. Drapion, like Stunky, is only weak to Ground. And it's just a pain to fight in general, do what you can (if you have the TM, your Dialga can learn Earthquake if I'm right).
A single good Grass type can pwn all of Bertha's (who uses Ground) pokemon. If you want, though, Water works too on some of them. Oh, and Hippowdon has a Sitrus Berry, so if you have Pluck, use it (Your Flying Pokemon will be immune to the Earthquakes as well, which I think all of her Pokemon might know).
Flint likes Sunny Day and he's going to try and get it out. If you can, stop him. If you can't, use alternatives to Water. Oddly enough, only two of his Pokemon are Fire. He's the easiest one, I think. You'll beat him more easily.
Lucian is no fun. Actually, with the right moves you can do really well against him until he whips out his Bronzong, and then whip out the Infernape and Flare Blitz (since you have it at 68) to your heart's content.
The Champion isn't bad. Use whatever you can on Spiritomb (Roar of Time is probably your best bet, or another STABed move). Roserade is a pushover. Infernape will toast it, and should be fast enough to move first. Gastrodon, again, is going to die in one good grass attack (If you have Roselia/Roserade, it's all about the Giga Drain). Lucario, while a very nice Pokemon, is also going to die to your Infernape, being weak to both Fire and Fighting. Milotic knows Ice Beam, so use Electric pokemon and not Grass. And Garchomp is weak to Dragon and Ice. Unlike my Palkia, your Dialga is not weak to Dragon, but it's not resistant either. No matter the case, a solid Ice Beam or Roar of Time will more than likely send Garchomp packing.
My recommendation is to use:
Infernape
Gastrodon or whatever other Water-type you can raise up
Dialga
Roserade
Alakazam (if you don't have a strong Psychic pokemon, go catch Azelf)
Luxray (you'll use Crunch more than you will Spark or Discharge)