。
She gradually got more and more arrogant.
Literal
She [topic-は] gradually attitude [subject-が] big became.
態度がでかい (literally 'attitude is big') is a colloquial expression meaning overbearing or arrogant — someone who acts above their station. でかい is informal slang for 大きい, giving the sentence a casual, probably frustrated tone. The ~くなった (became) marks the change of state, and 徐々に (gradually) indicates this wasn't sudden but a creeping transformation over time — the kind of slow change that builds someone's irritation.