After beating Jerry or Rhona (you don't need to face both, but really should- missing out on a chance at experience points is not a wise decision in most games) you'll gain access to the upper two feet of the vertical dragon statue.  Here you'll find a pair of battles for each of which you must use three pokemon at the same time.

The upper left foot holds a Rotation Battle expert.

Battle: Veteran Denae (3520 Poke)
Opponent: Fraxure Lv 44, Druddigon Lv 44, Axew Lv 44

Denae's Druddigon is really the least of your worries here- both her Axew and Fraxure use Dragon Dance pretty frequently, and she often switches away from them after several Dances to leave you guessing as to whether you should be ready for an attack on any given turn.

The upper right foot holds a Triple Battle expert.

Battle: Veteran Ron (3520 Poke)
Opponent: Fraxure Lv 44, Druddigon Lv 44, Axew Lv 44

Ron's Axe dragons both use the Mold Breaker ability, which can make things a bit rough if you're relying on type immunities in this battle.  Thankfully, Ron's 'expert' skills apparently don't extend to using his three pokemon in tandem with each other or in ways that boost one another, so you shouldn't have much of an issue here.  This is definitely an easier and faster battle than facing Denae.