There is no magic technique. you need to isolate the element with rotoscoping or keying and then stabilise it.
And how to do rotoscoping or keying?
After that shall I use warp stabiliser or stabilising motion or stabiliser through a motion tracker?
Depending on the movement, this can be done in CS6 by applying 2D stabilisation then reverse it. You just need track the eyes. Andrew Kramer has a tutorial that uses this technique, http://www.videocopilot.net/tutorials/demon_face_warp. For CC version this is how you do it Remove camera shake with the Warp Stabilizer VFX | Adobe After Effects CC tutorials.
To lock the movement of an object simply track the object you want to lock into position then apply the tracking data. You do this in AE with the Tracker panel which you find under the Window menu or by selecting a layer in the Timeline and going to Animation>Track Motion. In the Tracking Panel you select the source you want to track and the type of track you want to do. Then you either Track Motion or Stabilize Motion. In the Track Type pulldown you'll find five different types of tracks. You also have to decide if you want to track just position, or position and rotation, or position rotation and scale. The selections depend on the shot and what you want to do with the shot.
If I am going to do some manual rotoscoping or want to apply specific effects to someone's head then I would probably track position, rotation and scale, then apply my effects, then use a null, some expressions and parenting to remove the stabilization and attach the effects to the persons head. Here's a quick example of how to do that. Sorry, I haven't had time to add the audio track to this tutorial yet.