Aigul Akhmetshina likes to describe herself as “just an ordinary girl from a small village in the middle of nowhere in Russia.” At 14, she left home to study singing in Ufa, the nearest large city more than 100 miles away, where she supported herself at odd jobs like handing out flyers while walking on stilts. Now 27, this “ordinary girl” is taking on one of the highest-profile operatic assignments imaginable: Headlining a new production of Bizet’s ever-popular masterpiece “Carmen” at the Metropolitan Opera opening on New Year’s Eve.