。
She gave it a try on her own.
Literal
She [topic-は] [by-herself-自分で] it [object-を] tried-doing.
やってみる combines やる ('do' — slightly more casual or colloquial than する) with the auxiliary ~てみる ('try doing X to see how it goes'). The past form ~てみた frames the action as a completed experiment whose outcome is no longer in question. 自分で here means 'by herself, on her own initiative,' implying nobody told or helped her — the で is the instrumental/means particle, framing 'oneself' as the means by which the action was carried out.