。
She grew up in the rough environment of New York City.
Literal
She [topic-は] New-York-city [genitive-の] harsh environment [in-で] grew-up.
育つ ('grow up, be raised') takes で for the location of the upbringing — the で of setting. 厳しい ('strict, severe, harsh, demanding') is one of those single Japanese adjectives that covers a wide semantic territory English splits up: 厳しい先生 ('strict teacher'), 厳しい寒さ ('harsh cold'), 厳しい現実 ('grim reality'), 厳しい環境 ('rough environment'). The 環境 ('environment, surroundings') here is broad — physical, social, economic. ニューヨーク市 (with 市 'city') is a slightly formal way to specify the city as opposed to the state.