I have already cleared challenge 6, the first time I tried it was after completing the game on normal and clearing all other 5 challenges... I had some problems with challenge 4 and had to retry like 10 times... challenge 1,2,3 and 5 were kind of easy as they took me around 3-5 retries each (except for challenge 5 which I cleared in my first try xD).
Challenge 6 was the hardest, the first few tries I tried it I couldn't even get past the second wave until I learned that an EMP emmitter would kill the flying robots instantly. After that, I kept dying on the third wave... I tried for like 3 hours until I got tired and turned my PS3 off.
The next day I tried again for like 1:30/2 hours. During that time I learned that the disk launcher could behead the Romanovs and that they would die after a while. I also managed to get to the last wave with the 2 bogeys but I couldn't beat them. Turned my PS3 off and decided that next time I played the game I would clear hard mode.
After a few days I cleared hard mode, got the trophy for clearing the game on hard and went back to challenge 6. It was kind of late and dinner was almost ready but I played for a while anyways. I couldn't clear it before dinner, so I went to have dinner (left the game paused) and went back to it. After a few more tries I finally cleared the challenge. You can see in my trophy card that there's a 2 hours gap between the Tactical Challenger trophy and the ARS Operator one, that's the time it took me to have dinner and clear the challenge after beating the game on hard :P but if you sum up all 3 times I tried challenge 6 before beating it I would say it took me around 7/8 hours total xD
I tried God Hard mode, but I still haven't cleared it. I played it for a whole evening until I got Act 2 Chapter 2. I haven't played the game since then because I wanted to get the platinum in Castlevania: Lords of Shadow... and now that I also have Resonance of Fate, I'll probably play it after I'm done with Castlevania and return to Vanquish after RoF.