。
She glanced shyly at the young man.
Literal
She [topic-は] that young-man [object-を] embarrassed-looking [adverbial-に] briefly looked.
恥ずかしそうに combines the visual evidential ~そう (attached to 恥ずかしい) with the adverbial に — 'in a shy/embarrassed-looking manner.' ちらりと is a 擬態語 for a quick fleeting glance, with the adverbial と marking it as an adverb modifying 見た. The combined image: a furtive, shy look — the kind given by someone interested but not wanting to be caught looking. ちらり / ちらっと are extremely productive mimetics for any momentary, fleeting, glancing action, including glimpses, brief thoughts, or barely-heard sounds.