。
She sighed at her unhappy fate.
Literal
She [topic-は] her own unhappy fate [at-に] sigh [object-を] put-out.
ため息をつく ('to sigh,' literally 'to put out a sigh') is the standard collocation for sighing — つく ('to attach, put') is the verb that conventionally pairs with ため息. The に here marks the cause/target of the sigh ('sigh at X'), one of に's productive uses for emotional reactions to a stimulus. 不幸な運命 ('unhappy fate') sounds somewhat literary — at home in a novel, melodrama, or memoir — rather than everyday speech.