Originally Posted by Fat Sprocket
According to the official players guide, it's merely "Try the Battle Subway 100 times or more". It doesn't say anything about winning 100 times in a row.
I love that there are medals for using Splash and Struggle.
Also apparently medals for catching a Pokemon with Pokerus. I have a feeling that is different than simply possessing a Pokemon infected with Pokerus.
This is the list I'm going by, and the medal says "Reach a streak of 100 in the Battle Subway".