I'm... willing... to concede this one to Alduin.
The only angle I can give to Green Arrow is that he would likely be allowed to use specialty arrows from the Zelda universe in this battle, but even then it's not a very good angle.
Light arrows effect Ganon because he's drawing upon dark magic to enhance his abilities, Alduin is just a dragon. Alduin doesn't survive on dark power, a light arrow would probably bounce right off him. Silver arrows would likely do the same thing, silver doesn't have any kind of special effect on a living dragon.
I can't justify Green Arrow having an enchanted arrow designed to slay dragons, because those only exist in the D&D world. That would be the only way that Green Arrow could have a chance.
A seasoned warrior can take down Alduin in Skyrim, becoming that kind of seasoned warrior would require extensive training in the Skyrim universe. Green Arrow has never taken down a larger opponent like Galactus all on his own, while Alduin literally eats warriors of Green Arrow's caliber for brunch.
I really wanted to find a way for Green Arrow to have a valid chance of winning this one, but he doesn't. Dragons are ridiculously tough on their own, and Green Arrow is taking on a dragon who can make other dragons obey out of fear.
Alduin obliterates Hyrule Caste, and Green Arrow with it.