If you have a TEFL certificate, does it matter which degree(s) you have?

I read that in order to teach English in a foreign country you need to have a BA in addition to a TEFL certificate, but does it matter which degree(s) you get? I'm thinking about teaching in Russia, and right now I am double majoring in Russian Language & Culture and Global Studies. Aside from a degree, what else could I do to increase my chances of landing such a job?