Kanto Battle Frontier
It was hatched as an Eevee in Time Warp Heals All Wounds from an Egg May received from a day-care worker in May's Egg-Cellent Adventure. Since then, it had become a major part of May's team, watching every one of May's Contests since it has hatched.
Eevee made its Contest debut in What I Did for Love, where it went up against Brock and his Marshtomp. Although Marshtomp, being part Ground-type, could detect where Eevee was when it used Dig, Eevee eventually scored a win for May.
Eevee also took part in the Kanto Grand Festival battle rounds in Thinning the Hoard! where it showed great battling skills and impressive synchronicity with May's Munchlax being able to combine its attacks with Munchlax's to take down Harley's Cacturne and Wigglytuff.
Sinnoh
In A Full Course Tag Battle!, May introduced her newly evolved Pokémon soon after she got reunited with the gang. She revealed that her Eevee evolved into a Glaceon by coming into contact with the Ice Rock near Snowpoint City. It was called out once again in order to help out Roman and Kylie in retrieving the restaurant's stolen food, where it battled alongside Dawn's Buneary. Both of them started off with a double Ice Beam, causing James's Carnivine and Jessie's Seviper to freeze. Followed by its Iron Tail and Buneary's Bounce, they blasted off their opponents.
In Strategy With a Smile!, May used Glaceon in the finals of the Wallace Cup, where it went up against Dawn's Piplup. The battle concluded with Dawn as the winner, though Glaceon lost the match by only a few points. During this time, Dawn herself (when she first saw it) commented that Glaceon was very cute.
May's Glaceon, as and Eevee had the typical traits of an Eevee: Playful demenaor, affection for it's trainer, loyalty, and quite energetic. Being a recently hatched Pokémon at the time, Eevee had great curiosity as it was fasinated by the ocean. Upon Evoulution it's Personality changed moderatley. While Glaceon retained it's loyalty and affection for its trainer, Glaceon's playful demeanor had been replaced by a more assertive and slightly agressive one that shows mostly during battle.