So pretty much the title. I've read that instances of individual archery duels between samurai were common during the time but how would that work in the heat of battle? Assuming I was victorious in this duel how would I go about collecting my foes head as proof of my glory? Would I have my retainers rush over immediately to collect or would I wait to the end of battle, and if I do wait how do I ensure no one tries to claim my trophy as their own?
You would most likely just fight whoever you find, regardless of rank. See here
After the battle, there would be head viewing ceremony for the most important heads, to identify them and reward their takers. If you didn't collect such important heads, you'll probably show the one or two heads you took to your general or his staff. Depending on the size of the engagement and the general's rank, he could either reward you then and there or report it up, and you'll be rewarded as deemed appropriate. If you lost the head in battle you'll probably try to find someone who can act as a witness to come with you. If you didn't take any heads (which would be most people), you can also have a witness to your exploit, show damaged equipment, horses, and/or wounds. Otherwise you just have to hope your story would be believed. If you're unsatisfied with the outcome you'd take your case to Kamakura to make your case and hopefully get some (or better) rewards, as Takezaki Suenaga did after the first Mongol invasion.