。
She had no choice but to accept her fate.
Literal
She [topic-は] fate [object-を] accept-only didn't-exist.
~しかない is a fixed pattern combining しか ('nothing but / only') with the negative ない ('isn't / doesn't exist'). Together they give the meaning 'there is nothing but X' = 'no choice but to X.' The literal logic is striking: the sentence frames acceptance not as an active choice but as the absence of any alternative — a quintessentially Japanese way of expressing resignation. 受け入れる ('to accept / take in') is itself a compound verb (受ける + 入れる, 'receive + put in'), the standard verb for accepting circumstances, conditions, or outcomes that are imposed on you.