I have found a Christian girl who I am dearly in love with. She is a prostitute. Even though she is not chaste, I really want to marry her however she doesn't want to convert to Islam. If we carry out all of the necessary conditions for a valid Islamic marriage, can she repent her sins without converting to Islam? Would this make the marriage valid?
Allah (ﷻ) said, والمحصنات من الذين أوتوا الكتاب من قبلكم إذا آتيتموهن أجورهن محصنين غير مسافحين ولا متخذي أخدان "And [lawful in marriage are] chaste women from among the believers and chaste women from among those who were given the Scripture before you, when you have given them their due compensation, desiring chastity, not unlawful sexual intercourse or taking [secret] lovers" (5:5).
This verse makes chastity a condition.
Thus in the scenario you described, the only thing making the potential marriage invalid is the fact that she is a prostitute. If she gives up prostitution entirely, repents and remains chaste thereafter.. then you may marry her and the marriage will be valid per Islam [since Islam allows marriage to women among the People of the Book].
So to make the marriage valid, she needs to repent and give up prostitution.
That said, some friendly advice: I would say to be wise and think about who you desire to marry. Because this person is going to be raising children and affecting their faith and actions, ultimately. Love can sprout with many different people, but not everyone with whom it spouts will take you towards Jannah.