I too have had an issue with this challenge.
A friend and I co-op'd 4 sets last night ... 2hr 8mins it took.
So you can imagine how freaking annoyed we were when the challenge didn't register
The challenge reads 'Complete four sets on any Firefight map in co-op play on Heroic or harder.'
And we did exactly that. On Heroic as well.
I think what has happened is that they didn't specify what type of Firefight game that you had to play. Gruntocalypse? Rocketfight? etc
So I don't think it's possible to play four sets in 20mins or 40mins. Our first set (as denoted by the voice saying 'New Set' at the start of set two) took 28mins.
We died a total 22 times (20 for my pal, 12 for me), my pal had 865 kills, I had 646 I think. And we cleared two bonus rounds at the end of the third and fourth sets.
Anyways ... we won't attempt it again because we've done it once ... and we can't be sure that it won't fault again and not register the challenge.
-dave