Kirito wins this, easily in fact, that I'm surprised you guys really went to the extent you did with no research. Let's start with the first thing, Kirito would find where The Hunter is first via the Searching skill. The searching skill allows users to detect enemies and players within a large range of them, allowing Kirito to find enemies within an entire forest. This includes enemies obscured by trees and whatnot.
So, a 20-meter range is nothing for Kirito, searching would allow him to find the hunter easily and move to dispatch him. But, another important part? The hiding skill, gives him stealth mastery, something he would certainly use against an opponent he can't immediately reach.
Now, the real nail in the coffin? Doesn't matter if the hunter has a gun, Kirito would notice it with his Searching skill and could use the
Spinning Shield sword skill which blocks projectiles. This is especially important if he gets noticed while sneaking up on The Hunter.
It doesn't matter if the hunter moves away, Kirito will just keep moving towards him, and eventually kill him, analytical prediction will also help with dodging/defending against the bullets. The Hunter is getting owned by Kirigoat here.
It's also important to note, that a bullet to Kirito's head may not have the same affect as it would on a real person. As a game avatar, he lacks real anatomy/organs to make it matter. To him, it's just another normal attack that passes through him, not something instantly kills him and weakens him because that's not how SAO does hit detection.