、。
Little by little, she gave way to despair.
Literal
She [topic-は] gradually, despair-mode [become-になった].
捨て鉢 (sutebachi) literally means 'thrown-away bowl' — the image of a vessel hurled aside in resignation. Figuratively it names the mental state of giving up on caring about consequences, the resigned 'whatever happens, happens' attitude that comes after wearing oneself out. 捨て鉢になる is the standard collocation. The comma after だんだん is rhythmic punctuation, slowing the pace and giving the sentence a drawn-out, reflective feel — a literary touch you'll see in narration more often than in dialogue. The verb ~になる ('become') with this kind of abstract emotional noun frames the despair as a state she fell into rather than something she actively chose.