。
She won first prize in the race.
Literal
She [topic-は] that race [at-で] first-place-prize [object-を] obtained.
獲得する ('to acquire, obtain, win') is a heavier, more triumphal verb than plain 取る or もらう — fitting for prizes, championships, gold medals, citizenship. Compare 賞を取る (lighter 'won a prize') with 賞を獲得する (more emphatic, official-sounding). The で here marks the venue / context of winning — 'at the race', not 'with the race'. 一等賞 is 'first-place prize', stacked from 一等 ('first rank') + 賞 ('prize'); 二等賞 is 'second prize' and so on. レース is the loanword for race, ubiquitous in athletic and racing contexts where 競走 would be the native equivalent.