。
She was raised in luxury.
Literal
She [topic-は] luxuriously was-raised.
贅沢に (ぜいたくに) is the adverbial form of the na-adjective 贅沢 ('extravagant, luxurious'). そだてられた is the passive of 育てる ('to raise/bring up'), written in hiragana rather than kanji. The passive shifts focus to her as the recipient of the upbringing.