。
She brags about being a good swimmer.
Literal
She [topic-は] swimming [subject-が] skilled is [nominalizer-の] [object-を] is-bragging.
自慢する ('to brag, boast') takes its content with を — ~を自慢する. Here the content is the nominalized clause 泳ぎが上手なの ('that her swimming is good'); の after な-adjective + な (the attributive form, na-adj→nan/nano with の) packages the whole adjectival predicate as a single noun-like unit for the wrapping verb. ~ている marks this as her ongoing habit, not just a one-off boast — she's the kind of person who keeps mentioning it. 泳ぎ is the masu-stem of 泳ぐ used as a noun ('swimming as an activity').