If the normal methods of unlocking the medal options is too hard for you, you can always do it an alternate way. These methods do not gain you the medals, but instead merely unlock the bonuses gained by them.

Bronze: Complete Original Mode with Sakura 8 times
Silver: Complete Original Mode with Vega 8 times
Gold: Complete Original Mode with Ryu 8 times
Platinum: ''vs. Vega II'': Win 4 battles, ''vs. True Vega'': Win 4 battles