1.
If someone suffers martyrdom, they are killed or made to suffer greatly because of their religious or political beliefs.
...the martyrdom of Bishop Feliciano...
He suffered martyrdom by stoning.
N-UNCOUNT
2.
If you describe someone's behaviour as martyrdom, you are critical of them because they are exaggerating their suffering in order to gain sympathy or praise.
She sat picking at her small plate of rice salad with an air of martyrdom.
N-UNCOUNT [disapproval]