Anime
Greta appeared in one episode of the anime. She's a spirited, tomboyish young girl who's very passionate about Pokémon battles. She also runs a karate dojo as a parallel activity. According to Scott, her role models are Chuck and Brawly.
Greta's sole appearance was in Wheel of Frontier. Before the battle, a wheel is spun to decide how many Pokémon will be used. While battles are single battles, the other Pokémon intended to be used remain outside of their Poké Ball until they faint. A running gag of the episode was that Ash and Greta were very similar in personality, both being fiery and passionate about battles.
Greta used a Hariyama and Medicham in her battle against Ash Ketchum. After a hard fought battle, Ash was able to win the Guts Symbol.
When Team Rocket interrupted the battle, she was already aware of who they were. She used her Medicham to send them flying after one attack.
Manga
As in the anime and games, Greta is the leader of Battle Arena. She owns a Heracross, a Shedinja and an Umbreon. She is also an animator in the Battle Frontier.
(Source: bulbapedia)