How do I level my dragons past level 10?

Solution 1:

You need Shrines to level dragons past level 10. Shrines allow dragons to level to level 15 after one condition is met, and then allow a max level of 20 when a second condition is met.

Once you have a shrine, you'll see a counter counting how many level 10 and level 15 dragons of the matching element you have. Once you hit 50 level 10/15 dragons for that type, you're permanently allowed to upgrade dragons of that type to level 15/20. All dragons you've ever had count toward the total; if you sell level 10 dragons they still count toward this total, even if you had them before the Shrine or even if you sell the Shrine.

Shrines only work for dragons which have their specific element; a hybrid Earth Fire dragon is covered by both the Fire shrine and the Earth shrine, and it's level counts towards progress on both shrines.

The Dragonvale Wiki has a list of Shrines and their costs/level requirements, but you start unlocking them at level 18 with the Plant shrine and unlock one element;s shrine every level after that, until level 25. They start at 500,000 and increase in cost by 500,000 cash each new element.

Fun Fact, the shrines change color when you meet goals; they start Bronze, turn Silver once you have 50 level 10 dragons, and turn Gold once you get 50 level 15 dragons.