Do you think Hester is a martyr, or do you think her repentance is sincere?
I am not sure that these two ideas are necessarily in opposition to each other. Let us explore each and then decide where Hester fits into the picture. A "martyr" is someone who is innocent and who suffers (and is usually killed) for the faith or for some saintly purpose. A person who shows sincere "repentance" is someone who is guilty, but shows they are truly sorry for what they have done. The true opposition here is in the terms innocent vs. guilty.
In my opinion, Hester is both; however, let me transpose the two terms in order to explain my theory. Yes, Hester shows sincere repentance. Hester is "guilty" of the sin of adultery for sure. She has Pearl after having relations with Dimmesdale. How does she show sincere repentance? By accepting the town's punishment without question. She stands on the scaffold. She wears the letter "A." She lives apart. She accepts isolation. However, yes, Hester is also a martyr. Even though she participates fully in the punishments of the town, the town punishes her for a lifetime for her sin anyway. Because everyone is a sinner, Hester becomes a martyr for the faith in this way. Every one of those townspeople sins in some way. Hester's sin is worn on her breast. She continues to be punished both by her letter "A" and by the looks of the townspeople. This makes her a martyr.
In conclusion, I should point out that Hester isn't necessarily "innocent," but she has been washed clean of her sin by reparation and is not any more deserving of sever punishment than any of the other townspeople. The townspeople aren't innocent either. In regards to sin, no one is "innocent."