Taken from the fewmiles/AA website:

Got points? - The Challenges are based on Q-points only. There's no Q-miles based Challenge (discontinued mid-2000) and no segments-based challenge either.

I just got off the phone with AACS and the guy told me to do the Gold to Platium challange I needed 10000 Q-points OR 16000 miles OR 32 segments. So I'm going for the 16000 miles. Hope this helps a few.