Accidentally stumbled on a much easier and quicker solution for all the par time achievements. I don't know if this method is bugged, requires you to complete each level on Legendary or something else, but this is what I did and the par time achievements have popped.
From the menu go into the Reach campaign, select your mission and choose rally point Charlie where you can. I put the difficulty on easy, and after simply completing the third segment of the level in as short a time as possible the achievement popped during the end level cut scene.
This worked for all levels where you can choose the rally point. Saves you running through the whole level.