I'm sure your teeny little sword is a real concern for him.

The dragon is pretty much the grand poobah of mythical monsters. Nothing else gets as much press, nothing commands as much respect, and nothing quite measures up to a 50-ton winged lizard that can breathe fire. They’ve been the classic fantasy villain ever since Beowulf went toe-to-toe with one in the 7th century or so. No hero throws around as much clout as one who says he hunted and killed a dragon. There is a pretty good reason for that, too: it would be practically impossible for your standard medieval hero to do so.

For starters, lets leave out all discussions of magic for the moment. As soon as we throw magic in the mix, anything is possible, so there’s little point in discussing it. If you like, we can say the dragon’s magic cancels out the hero’s magic and leave it at that. What we’re looking at here is whether and how a person with access to the standard armory of the pan-medieval fantasy world could kill a dragon.

The Dragon’s Defenses

Okay, so let’s size up the opposition. Dragons are reputed to have the following capabilities: 

1. Massive Size: Dragons are usually said to be 20 feet long or longer, putting them on par with dinosaurs or whales–10 tons at the low end, maybe even 100 at the high end.
2. Armored Scales: Dragon scales are thick, flame resistant, cover the majority of the body, and are hard to get through. Some places they are described as ‘hard as steel’, though we can presume this is a bit of an exaggeration.
3. Flight: Dragons have wings and can fly. This is a major advantage, obviously.
4. Intelligence: Dragons are fairly smart. In some cases they are shown to be as smart as people, while in others they are simply very cunning predators of standard animalian intelligence.
5. Fire Breath: Perhaps the most dangerous aspect of the dragon is its capacity to breathe fire. Any attempt to slay a dragon needs to take into account some way to survive a blast of flaming breath (which, we can presume, operates more like acid or napalm than simple fire, as those are more plausible explanations).
6. Teeth, Claws, etc.: To top all that off, the dragon still has the standard array of deadly claws, fangs, horns, and so on that should be sufficient to pulp anybody who messes with it, anyway. 

Given this, no sane individual (or team of individuals) would go after a dragon. Just give it the virgins, already, and move on with your lives. Points 4 and 5 alone are sufficient to guarantee that any idiot wanting to kill a dragon will be dead long before he’s finished challenging it in the name of St. George. They don’t make stuff in the middle ages that can take a soaking in napalm and let the user walk away. Nevertheless, if the dragon needs killing, folks are going to try anyway. Let’s consider their weapons.

By Sword

Don’t be an idiot. Even provided you do make it past the flaming breath and it happens to stay on the ground and you don’t get crushed by giant claws or gobbled up by a giant fang-rimmed mouth, you’ve still got the scales to get through. Even if you do that, what makes you think the sword will actually kill it? If it’s a sufficiently huge dragon (like, Brontosaurus sized) it’s going to take you a long, long time to hack it to death with a sword. It would be like trying to kill a person with a dessert fork–you could do it, sure, but the person pretty much has to be tied up and you need plenty of time and/or a keen grasp of human anatomy. Try hunting a dragon with a sword and kiss your butt goodbye.

By Spear/Lance

 Better, certainly. The weapon is larger and longer, meaning you have a chance of puncturing something vital with a

Now *this* I can believe. 5 people versus one young hatchling. Good odds.

strike. This is how they kill whales, after all, and so it’s not entirely without merit. It can still fly away, though, and can still melt you with fire, and it’s still armored in a way that whales aren’t. Furthermore, the way they actually managed to kill the whale with the lance was to harpoon it, exhaust it, then move in and kill it. Given flaming breath, flight, and all that, it seems unlikely you could pull this off with a dragon. If you were to do it, you’d need a big team of people (like a series of whaleboats, except on the ground) working in coordination and you’d need a dragon to be no smarter than your average whale. As a lone dragonslayer? Forget it.

By Arrow

Let me put it this way: Bard got stupidly lucky with Smaug. Skilled hunters do use bows to hunt large game like Cape Buffalo, but a Cape Buffalo is tiny compared to a dragon. Furthermore, such hunters today are using modern bows and modern arrows that maximize the kinetic energy needed to kill (read this article for more on the physics of hunting large game with bows). Granted the bow keeps the dragon from being able to fly away as easily, bypasses some of the dangers from flaming breath and the teeth/claws, but it is going to have a hell of a time penetrating the dragon’s hide by enough to wound it in any mortal capacity. You’d need dozens and dozens of skilled archers with the most powerful bows and sophisticated arrows in the world, and even then they’ve got fair odds of being roasted.  

Conclusion

Essentially, the lone dragonslayer thing is extremely unlikely to the point of being implausible without the use of the idiot ball in some way. You’d need a team of dedicated professionals using things like siege engines, laying traps, and, most importantly, using dirty tricks. Poison its water supply, collapse its cave on top of itself, or, of course, some kind of magic. Beyond that, you are fresh out of luck.

Now, much of modern fantasy lore is well aware of this. George RR Martin points some of this stuff out in A Song of Ice and Fire, and, in one of my personal favorites, Barbra Hambly explores just how impossible a task this is in her 1985 novel Dragonsbane (which I recommend, though I haven’t read it since high school and my memory of it may make it seem better than it is). It should be noted, even, that Beowulf himself died in his struggle with the dragon (though he killed it with a dagger) and had help from his friend, Wiglaf. In any event, I feel it is important to give dragons their due when trying to take them down–the frontal assault isn’t going to work, guys, and you’re going to need help.