。
She's so careful that she rarely makes mistakes.
Literal
She [topic-は] very attention-deep [because-ので] rarely mistake [object-を] does-not.
注意深い stacks 注意 (attention) with the suffix-style 深い (deep) — 'deeply attentive,' i.e. careful. The same shape gives 興味深い (deeply interesting), 感慨深い (deeply moving). めったに...ない is the textbook 'rarely' frame — めったに alone is meaningless; it always needs the negative verb to deliver its meaning. Removing the negative leaves the sentence ungrammatical.