I have to agree with others here. Sprint is not necessary at all, even after he begins to speed up. So long as your behind him, you can tightly circle behind him as he moves.

I did this quite a few times last night and had no issues without sprint (because the lot rules right now sucks, so I am stuck there, lol).

If your having issues, I would try and cut those corners of the boss earlier if he starts to get too close xD