If there is no self what or who is it that gets enlightened? From reading this answer I come to understand that anatta means the lack of a core that can be conceived as self. If there is no permanent self, then who or what gets enlightened?
The main point of the answer you cite is that anatta is a characteristic of ultimate reality. Your question misses this and conflates two different paradigms or levels of understanding.

In Theravada Buddhism we recognize two levels of truth; conventional truth (sammuti-sacca) and ultimate truth (paramattha-sacca). Conventional truth relies on a spatio-temporal paradigm, in which there exist people, places, and things. It is the level on which "you" and "I" exist, and it is the level on which a "person" becomes "enlightened". None of this has anything to do with the characteristic of non-self, which works on the level of ultimate truth. Ultimate truth relies on an experiential paradigm, in which there exists only the momentary experience of seeing, hearing, smelling, tasting, feeling, or thinking. 

So, the answer to "who becomes enlightened?" is "a being becomes enlightened." As to how that can be reconciled with the teaching on non-self, there is really no conflict, since non-self describes a characteristic of ultimate reality, at which level concepts like "being" or "enlightened" have no place.