From Bulbapedia, the community-driven Pokémon encyclopedia.
A Grand Duchess (Japanese: グランダッチェス Grand Duchess) is a type of Pokémon Trainer that debuted in Generation VI. This Trainer class is a title of nobility, granted in the Battle Chateau, and Trainers with this class only appear there. Grand Duchess is the highest rank of nobility for females, ranking above Duchess. They are the female counterparts of the Grand Duke class.
The female player character may earn the title of Grand Duchess by defeating most of the Trainers in the Battle Chateau. Diantha is the only non-player character who uses this Trainer class. She can be battled after the player has reached the rank of Grand Duke/Grand Duchess in the Battle Chateau.
Pokémon X and Y
An active writ in the Battle Chateau may change the levels of Diantha's Pokémon and the reward she gives. See here for the parties when a Writ of Challenge is active.
In the anime
The title of Grand Duchess was mentioned in Breaking Titles at the Chateau!, where Viola and Grant battled each other for the highest possible rank. However, since Grant won the battle, Viola wasn't able to become a Grand Duchess.
In other languages