Lady Snowblood

Her name is Snowblood, child of vengance.

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. Yuki never knows the love of a family but only killing and revenge.