This achievement is Story Related and therefore unmissable.
The achievement is entitled "No Happy Returns" and is earned automatically once you first return to Wonderland. Once you gain control of Alice from the intro, you will wander the streets and eventually begin following a white cat. The cat will lead you an alleyway where a series of cutscenes will play out. Once you gain control of Alice again, head over to the old woman and it's all cutscene from there,