She was in the depths of despair.

Literal

She [topic-は] despair [possessive-の] rock-bottom [at-に] was.

どん底 (どんぞこ) means 'rock bottom' or 'the very depths' — an emphatic compound where どん is an intensifying prefix (like the ど in ど真ん中) and 底 (そこ) means 'bottom.' 絶望のどん底 creates a powerful image: the absolute lowest point of despair. The verb あった (from ある) is used instead of いた because the sentence describes a metaphorical state or condition rather than simple physical location.