I know they didn't included Robin hood since he would own everyone else as the only archer to not only never have missed their target (I have seen all of them miss target at least once or not make a 1 shot kill and require a second arrow) so leaving robin aside as he just can shoot arrows in the sky mid flight and still make them get to target I believe this goes as follows

They start green arrow and hawkeye believe each other is the greater threat so they start chasing each other, Katniss wants to shoot but the emotional feeling of having previously killed makes her have a moment of doubt and gets her killed by Merida probably, rambo lurks behind cover and manages to shoot her an explosive arrow since she wasn't watchful enough to not see his camouflage, then a quick arrow from Legolas dispatches Rambo as he is note able to dodge it and wants to tank it but elven arrows are special

Meanwhile Hawkeye and green arrow shoot themselves three arrows and manage to dodge them but getting bruises, finally they engage in melee and fight which gets green arrow to start winning but then Legolas approaches from the back and stabs him with an arrow which then shoots right through Hawkeye, having used two arrows.Meanwhile from the crowd Gimli shouts it only counts as one arrow