Some important things that may help.
ONE RUN actually just means one game save. There is full mission select support and progress will be saved, so don't fret about missing it! (this goes for all "single run" achievements)
Also mine actually popped with one still left to do - the 10 barrel kills on The Necropolis
EDIT: An interesting note from namr3h, if you restart the mission (possibly only during first run through) in which you had completed some challenges, the game save will relock them, however, the achivement tracker saves the progress the moment a challenge is completed.
This seemingly explains my own experience as well.
Following on from that (and this is completely untested), you could in theory find some easy challenges and complete them repeatedly without ever completing the respective mission to save on effort on difficult challenges.
That said, the challenges aren't so hard, so your choice.