。
She is both a doctor and a mountaineer.
Literal
She [topic-は] doctor is-and mountaineer is.
AはBであり、Cである is the formal 'both A and B' pattern, threading two predicates with である ('to be,' the literary copula) — the first verb takes its 連用形 form あり, which functions as 'and' linking into the next clause. であり is markedly more formal than the casual ~で or ~だし: it signals biography, profile copy, or any dignified introduction. 登山家 ('mountaineer') uses the same productive ~家 suffix seen in 政治家, 芸術家, 夢想家.