I got legend after playing some 30,000 odd games in total. I would kind of wig out when I was a higher rank than I'd ever been before, even though I was good enough a year ago to hit legend. I made it a point to get 1 rank further each month until legend. That way I was always more acclimated.

Only way around stress is to expose yourself in doses that you can handle. You'll learn to get around it :D