。
She stubbornly refuses to compromise her convictions.
Literal
She [topic-は] adamantly belief [object-を] does-not-bend.
頑として is a fossilized adverb — the kanji 頑 ('obstinate / sturdy') plus the と of manner-adverb formation, plus して — used emphatically before negative verbs to convey unwavering refusal. 信念を曲げる ('to bend one's beliefs') is a fixed metaphor: principles aren't physically bent, they're compromised under pressure. Crucially, the negative form 信念を曲げない is almost always praising the person's integrity, not criticizing their inflexibility — Japanese, like English, treats unbending principle as a virtue when described this way. The sentence has a slightly editorial, almost biographical tone — the kind of line you'd encounter in a profile or eulogy.