This was one of the first racing games I ever played and I will still consider it as one of the best I've ever played. I remember this same challenge but I wasn't able to beat it after several tries.
But there was a certain challenge that my brother and I were able to beat after a lot of tries. It required you to use a Chevrolet Camaro and rack up a certain amount of bounty while on the highest heat level.
Oh, yes... that one is the last of the "challenge race". It is one of the hardest ones for sure. There is this other one where you have to evade the police after 30 minutes. That was the one which took me the maximum tries.
I don't think I remember that one, but that one sounds really difficult. I've always disliked those kind of pursuits because it's either I escape too early or busted