I'd suggest you use shadowplay or Action! (
https://mirillis.com/en/products/action.html) and use the time shift function to record gameplay. (if you're using a NVIDIA card, I beleive there are similar apps for Radeon)
Basically it works like a DVR, it's always recording and will keep a set amount of footage in the buffer (you can set the amount, say 10 mins), it'll discard footage falling outside the 10 min window, and you'd set a hotkey combo to save the fight footage of the fight you just had after it's finished.
So you'd launch, do your key combo for time shift start, fly, have a fight, and if you wanted to keep the fight footage, enter key combo to save last 10 mins, it'll spit out an mp4 that will include blackouts, the HUD etc, everything that was on your screen, which you can edit in your video editor of choice.
Have a peek at my channel (link in signature) and you can see examples of how it might look (except your shooting is better

)
Steely