Lady Snowblood (1973) on Netflix

Yuki's family is nearly wiped out before she is born due to the machinations of a band of criminals. These criminals kidnap and brutalize her mother but leave her alive. Later her mother ends up in prison with only revenge to keep her alive. She creates an instrument for this revenge by purposefully getting pregnant. Though she dies in childbirth, she makes sure that the child will be raised as an assassin to kill the criminals who destroyed her family. Young Yuki never knows the love of a family but only killing and revenge.