1. Swords are for parrying, not brute force. Swords are balanced so that their centre of mass is close to the hilt, which allows you to turn them quickly and easily in order to deflect incoming blows. That is very useful when fighting another human with a weapon, but not much when fighting animals. And the easily part means there is not that much energy in the swing, so it is not enough to significantly hurt anything of a size of an elephant.
2. To get more energy, you need either:
1. Thrusting weapon. You can thrust a sword, but a spear is longer for weight and sword is not giving you any advantage at this point.
2. Head-heavy weapon like an axe that you spin around, accumulating significant momentum, or raise high, accumulating potential energy. Disadvantage is that while preparing for the blow, you are not covered. With spear, the point is at least in front of you all the time, blocking access to you.
3. More manpower. That leads to a long pike carried by more than one fighter. But the coordination would be pretty difficult.
4. 358
A simple machine. Since the power of your muscles is still the limiting factor, you need to pre-strain the thing. The result is a heavy cross-bow drawn using a winch. This can finally be scaled to have whatever penetrating power you need, at the cost of slow reload time.
3. For how hard it is to kill a large beast, consider whaling. Before the harpoon gun, this involved throwing several harpoons at the whale with buoys attached to them. There was no way to hold onto the ropes—the whale would easily pull the men under. Instead, they waited—for hours—before the drag of pulling the buoys together with the wounds tired the whale so it was barely able to move and only then they finished it off with more spears.
Now this works on whales because they don't see the attack that is lead from above surface and can't retaliate effectively. But with a dragon that would be retaliating it would be much harder. You could attach on the ropes something that would get tangled to trees or stones and prevent the dragon from following when you retreat, but it could have enough power to pull the harpoon out and it would probably still have enough strength to fight back, so it would be very dangerous.
4. Or you can increase lethality by other means, like poison. Some potent poisons can be found in nature like on the poison dart frogs, or made with little resources, like curare. Something would surely be found that would work on the monster in question.
5. Either way, fighting monsters at range is much safer. If you have fire-breathing dragons, fighting them at close range would unlikely be survivable and if you have flying ones, you need ranged weapon to reach them at all anyway.
So my guess is that if an effective poison is available, poisoned arrows would be the main weapon of choice and if not, heavy crossbows, the later possibly firing harpoons with some kind of anchor at the end of the rope to slow the beast down.
And in either case, the fighters would probably be riding to allow them quick retreat if they missed—or if they've hit, but need to wait some time for the beast to die. 160