Where can you find and how to defeat Cynthia

Cynthia is the Pokemon League Champion.
She is encountered many times before you battle her in the Elite four however.
The first time you see her at the contest hall in Hearthome.

Her Pokemon includes a Lucario, Garchomp , Milotic and Spiritomb.
She also has Gastrodon and Roserade.
Pokemon League Champion Cynthia Squad
Spiritomb female Lv.61 Ghost/Dark NO WEAKNESS KNOWN NORMAL, FIGHTING, DARK DON'T WORK ON THIS POKEMON
Milotic female Lv.63 Water weak against ELECTRIC, GRASS
Gastrodon female Lv.60 Water/Ground weak against GRASS
Garchomp female Lv.66 Dragon/Ground weak against ICE, Dragon
Roserade male Lv.60 Grass/Poison weak against FIRE, Ice, Flying, Psychic
Lucario male Lv.63 Fighting/Steel weak against FIRE, Fighting