Instructions
Travel to the Trophy Garden of the Pokemon Mansion on Route 212. Talk to the mansion's owner to find out which Pokemon have been spotted in the garden that day. Eevee will only appear when it is the spotted Pokemon of the day.
Walk through the garden when Eevee has been spotted to trigger a wild Pokemon encounter with Eevee. Weaken Eevee using your best attacks and throw a Pokeball to capture it.
Increase Eevee's happiness level to 220 during the day to evolve Eevee to Espeon. You can increase Eevee's happiness level by walking around with it in your Pokemon Party, using Eevee in battle without letting it pass out, giving it special hold items like the Relax Ball and entering it in Pokemon contests.