。
When she was a child, she was very shy — like many of us were.
Literal
She [topic-は] child [time-のとき] we [genitive-の] many [subject-が] so-were [as-ように] very shy-person was.
A long sentence with an embedded simile clause. のとき ('at the time of, when') attaches to a noun to give a time reference. The middle clause 私たちの多くがそうであったように ('as many of us were') is a compressed reference — 'so' (そう) standing in for 'shy,' であった as the literary past of だ, ように making it a manner clause. 恥ずかしがりや is a charming compound noun: 恥ずかしがる ('act embarrassed') plus the suffix ~屋 ('one who has the trait of'), forming 'a shy person, someone who tends to be embarrassed.' The 屋 suffix appears in many personality nouns: 寂しがり屋, 怖がり屋, 照れ屋.