。
She tried to give swimming a go.
Literal
She [topic-は] swim let's-try [quotative-と] did.
Two attempt-flavored auxiliaries stack here. 泳いでみる is V-て+みる ('try doing'), where みる ('see') functions as 'give it a try / attempt and see what happens.' The volitional 泳いでみよう ('let me try swimming') plus と and the verb する (here in past form した) gives ~ようとする ('try to / attempt to'), which describes an effort — possibly successful, possibly not. The sentence as a whole reads almost like a layered 'she made an attempt at attempting to swim' — the two auxiliaries do partly overlapping work, which is acceptable but slightly redundant; tighter phrasing would drop one of them.