。
I became captivated by her beauty.
Literal
I [topic-は] her [attributive-の] beauty [attributive-の] captive [to-に] became.
とりこになる ('to become a captive, be captivated') uses とりこ ('captive, prisoner,' written 虜 in kanji). 美貌 ('beauty,' specifically facial beauty). The chain of の links 'her → beauty → captive.' A literary, romantic phrasing.