In order to get 100% for this mission you need to follow the same path that Mary Ann is taking. To beat her that way you need to get your stamina up by running around.

But if you just want to pass this mission you can take shortcuts. Shortly after you start jump over the fence:

Jump over the fence to get ahead of Marry Ann

When you get to the stairs avoid them and run or fall down the hill to the left of the stairs:

Run or fall down the mountain to get ahead of Marry Ann

Now winning shouldn’t be a problem. To run faster mash the sprint button as fast as you can.