In addition to the solutions mentioned above, there is a third method that I discovered accidentally while working on a different achievement. If you start the game on the PC version with the anti-cheat feature disabled (which enables you to use mods, although none are required for this method), do the following:
*Enable scoring or the timer and start the mission from the beginning (any difficulty should work, I was on Normal).
*Play to the end of the level normally, using whatever abilities you want.
*During the ending cutscene, press
to bring up the menu (this will pause the cutscene, you don't want to skip it), and select Save/Quit.
*Close the game and relaunch it with anti-cheat enabled (the only mode where you can earn achievements).
Once the level loads, you should be taken to the postgame carnage report (which is why you need scoring enabled), and the achievement should unlock here. Playing the level in "mod mode" (as I call it) means you skip all the flags that would void the achievement, so you can sprint and jetpack around to your heart's content. Simple as that.