。
She insisted that it was my fault.
Literal
She [topic-は] my mistake [is-だ-quotative-と] insisted.
言い張る is a compound verb (言う 'say' + 張る 'stretch / stand firm') meaning 'to insist, maintain stubbornly, refuse to back down from one's claim.' The だと marks the preceding clause as a quoted assertion: 'said 「it's my mistake」 and stood firm.' 誤り means 'error, mistake' — slightly more formal than 間違い, often used for errors of judgment, factual errors, or moral missteps. The implication: the speaker disputes the charge, and she's having none of it.