No gold medals required.
Time Attacks will take between 6-30 minutes depending on skill and if you're trying to achieve a gold medal.
All Normal Challenges are very easy if you apply the Zangief technique.
Level 14 will not allow Special Moves so:
(thanks to Rewmac)
Choose Dhalsim. Use down heavy kick and heavy punch all the time until you have a super or ultra wait for a chance and unleash it. I beat it in less than 2 minutes this way. This first opponent should be Honda (it was always for me). Keep you distance, guard a lot. The difficult part will be Akuma. When he unleashes his Ultra jump, if you can't avoid that then Pause, Retry. If he hits you your done for. If you get past Akuma you'll get it done. Watch the timer because you'll only get 5 seconds/match. Use Ultra if you have an opening. Just like Super, it will give you bonus seconds.