Transforming Eevee to Sylveon is quite a difficult task in Pokemon X and Y. However, a way to do that has finally been found.
In order to evolve Sylveon from Eevee, you will have to learn a Fairy-Type Move while using Eevee.
Along with that, you will have to raise the different Stats of your Pokemon. Pokemon Amie allows you to increase the different attributes like Enjoyment, Fullness, and Affection. Refer to our Pokemon Amie Guide to know more about raising these attributes.
In order to carry out the transformation from Eevee to Sylveon, you will have to raise the above mentioned attributes to the maximum possible level.
Once you have done all these three things; simply learn a Fairy-Type move and you will turn into a Sylveon.
You can refer to TheOneIntegral’s video to know exactly what to do: