You've probably noticed the "Complete 40 dungeons in X biome" quests as soon as you reach level 10. After a couple of these I noticed a little pattern.
First off, as soon as you see the quest pop up, load up a new world. I'm not sure about this but I think lower levels work, if you want to clear them out faster, however you won't get the uber bonuses.

A surefire way of completing these before the 20 minutes end is, after loading up the new world, look where the nearest biome you need is, head there, preferrably with some other players aswell to speed up the process and rush the boss on every dungeon. Just ignore the minions and kill the boss as soon as possible. If you do it right, you should be doing about 3 dungeons per minute, which is where the next step comes in.

If you have one of the classes listed as "BONUS", use them to get 2 points per boss instead of 1.

That's about everything I can tell you. So far I've gotten about 9 dragon souls using this method. It's not perfect and I will be accepting suggestions on how to improve the guide. If there's anything you feel could be improved, feel free to comment.

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It'll give you a class coin if you use it so, enjoy!