This sounds a lot like the concept of an AMV (Anime Music Video).
I don't think you could ever get the rights to such a video as long as the musical score is not your original content (parodies or cover songs). If the musical score is taken from another artist there probably needs to be established communication with whomever owns the intellectual property. Big artists usually mean big record companies as well. That's where the problem would be. These companies police youtube on their own, and put up claims to such content. The video will often remain if it is not a severe breech, with no harm to you, but you won't be able to monetize it.
It's been a while since I researched laws about intellectual properties and how these are governed on YouTube, however. So, don't put too much into my reply.