。
She has an intense interest in everything around her.
Literal
She [topic-は] surroundings [possessive-の] every thing [to-に] intense interest [object-を] is-holding.
身の回り (みのまわり, 'one's surroundings') is a set expression for what's close to someone in daily life. あらゆる ('every, all') is more emphatic and formal than すべての — it stresses totality. The expression 興味を持つ ('to hold interest, to be interested in') is the standard phrase, and 強烈な (きょうれつな, 'intense, powerful') elevates the curiosity from mild to all-consuming.