What should a young man do who wishes to marry a girl with a bad reputation, but she wants to repent and observe the Islamic hijab, while his parents strongly reject this marriage?

Marriage is a fortress for young people. If a girl who was known for bad conduct repents and becomes upright, there is no harm in marrying her. However, if your parents reject the girl because of her bad reputation, then obey them unless you fear falling into zina (fornication/adultery). It is advisable to look for someone other than this woman, someone whose religion and character are pleasing, in order to satisfy your parents. And make abundant supplication.