I'm sorry but the title of most badass archer can only go to one man.
The only man to tour Europe killing Nazi's with a longbow.
'Mad' Jack Churchill.
A real British WWII solider who spent the early part of the war leading small scale counter attacks on German supply depots and communications systems as every other unit was being slowly pushed back to the French coast. What makes that more impressive? He did it for the most part with only a motorbike, a bow, and a broardsword.
After Dunkirk he enlisted in the commando's and led a raid on Norway, playing "March of the Cameron Men" as he lept from the landing craft, grenaded an enemy position, and charged forwards.
2 beach landings later he took a occupied town in Italy taking 42 prisoners largely without a fight. He did that by creeping up to their position, aiming his bow at them, and telling them very loudly and clearly to give up. When asked about it he explained "I maintain that, as long as you tell a German loudly and clearly what to do, if you are senior to him he will cry 'jawohl' and get on with it enthusiastically and efficiently whatever the situation"
He, and all 42 prisoners, then marched back to camp with the wounded being pushed in wheelbarrows and on carts like something from the Napoleonic era.
He was finally captured in Yugoslavia when his attacking force was decimated. He was the last man alive lightly injured, but still had the strength to play "Will Ye No Come Back Again?" on the bagpipes until a grenade knocked him out. It was in that battle he became the last British soldier to kill an enemy with an arrow fired from a bow.
But that wasn't the end. After being sent to a concentration camp in Germany he immediately started to plan an escape. 2 attempts later he successfully walked 100 miles to the American lines and he requested reassignment to Burma as the nukes were dropped. His quote on that is perhaps the most bloodthirsty and unapologetically badass thing ever. "If it wasn't for those damn Yanks, we could have kept the war going another 10 years." Yeah. He wanted to war to continue. He wasn't fighting to win, or to beat the Nazi's. He was fighting because he enjoyed it.
After the war he was shipped to Palestine and fought again, saving the lives of around 700 Jewish doctors in the evacuations.
He retired after that, took up surfing, and reportedly threw a briefcase out of his train home every day.
He died in 1996 at the age of 89.
This has to be more badass, and all round better, than any fictional option. He was a real soldier that went around killing Nazi's with a longbow. Not even Legolas killed Nazi's with a longbow (And if he did I actually want to see that fanfic).
In fact, the Oxford definitions of 'badass' and 'hardcore' have both been replaced with just a picture of 'Mad' Jack Churchill holding his broadsword over his head as he leapt from a landing craft, screaming "COMMANDO!!" at the top of his lungs.