。
She was firmly resolved to resign.
Literal
She [topic-は] resign [volitional-ようと] firmly had-resolved.
辞職しよう (volitional of 辞職する, to resign) combines with 固く決心していた (was firmly resolved). 固く (かたく, firmly/solidly) intensifies the determination. 決心していた with ~ていた marks this as an established, ongoing state of resolve — her mind was already made up. 辞職 is the formal word for resignation from a position.