。
She glared at me with fury in her eyes.
Literal
She [topic-は] eyes [object-を] anger-causing me [object-を] fix-glared.
眼 (instead of the everyday 目) signals a more literary register — same word ('eye'), different kanji, weightier feel; you'd see this in fiction more than conversation. 眼を怒らせる literally 'to make one's eyes angry' is a fixed descriptive expression — 怒らせる is etymologically the transitive of 怒る ('be angry'), here applied reflexively. にらみ付ける is a compound: にらむ ('glare') + 付ける ('fix/attach'), much sharper and more committed than plain にらむ — the suffix ~付ける recurs across Japanese to mean 'do an action with full intent and attachment' (押し付ける 'press onto', 言いつける 'inform on'). Together it's a vivid, almost cinematic glare.