Note: Lao Shan Lung, Kirin, Yamatsukami or any monster that doesn't carry it's wound after a battle will not be included in this guide.
You do know that Elder Dragons, will flee after certain circumstances (Example : Kushala Daora). Now, did you know that you can use that as an advantage? How? Here's what you gotta do:
1. If you're not strong enough, have a friend to help you. Hunt one Elder Dragon together.
2. Make sure you cut the dragon's tail BUT do not kill the dragon. Make the dragon close to death as close as possible.
3. The Elder Dragon will flee. If it's really close to death, that's good.
4. Save your game. Then, if you find the same Elder Dragon (with the same or different quest), initiate the quest.
5. You should be able to kill it easily.
Conclusion: Yes, I guess you have the picture now. If you kill the dragon and didn't get the item you want (e.g. Big Elder Dragon Jewel), you can always reload your game, then initiate the quest until you get what you want. This way, you won't have to kill it for an extra period of time, and you get the "result" you want.
However, this 'trick' isn't really that positive for you. It will make you kill less dragon (which applied in your guild card).
Your choice, have fun :)