One who expresses (or the act of) feigned sympathy/interest in hopes of being recognized for it [duplicate]
Perhaps something like:
sanctimonious: hypocritically pious or devout. It's not exactly about "doing good", but I do feel it encapsulates the idea of being good (if in a religious manner) for show.
Have you considered self-serving:
serving one's own interests often in disregard of the truth or the interests of others
or sycophant:
a person who praises powerful people in order to get their approval
Pharisaical: marked by hypocritical censorious self-righteousness