While I haven't done anything like this, the following would be my approach:
Shoot the person and their reflection on green screen background (behind the actor and the actor's the reflection) in such a way that they are not overlapping. You may need to have the actor "walk" in place to give the idea she walks into the mirror. The actual horizontal movement will be added in AE. Separate both from background, move so that they overlap and it appears they are touching and animate one one way the reflection the other way while masking off anything that should disappear (anything beyond the symmetry plane) as the actor moves into the mirror. Create a static background plate so it looks like the background stays in place while the actor moves.