Use the long jump to stay ahead of him. While running, press R then B and you will do a low-arc jump that gets a lot of horizontal distance. It's the best way to keep ahead of that guy.

Another good tip is to always run up the grass hill at the base of the mountain instead of trying to follow him around the path. It seems like it takes forever, but it's actually a bit quicker. Just make sure you don't stop running while on the hill or you'll slide back down it and you'll have to start over.