To evolve your Sidekick dragons, you must have two one-star dragons at level 10 (the maximum level) of the same name. To evolve the dragon a second time, you must have a two-star dragon at level 20 (the maximum level) and evolve it with another two-star dragon at level 20 of the same name.
If you evolve two dragons of the same zodiac (marked in the top right corner of the dragon information screen), you will also receive a Zodiac Bonus that provides a bonus boost in damage! The first Zodiac Bonus evolution provides 25% bonus damage and the second Zodiac Bonus evolution provides 60% bonus damage. There are twelve different zodiacs:
Zodiac Bonus on the Second Evolution
In order to continue the Zodiac Bonus on the second evolution, make sure the Sidekick you selected to evolve has the Zodiac Bonus. The second Sidekick used to evolve the Sidekick selected first must also have the same zodiac displayed, but it does not matter if the second dragon has a zodiac bonus or not. It is important that you make sure that you select the Sidekick with the Zodiac Bonus first when evolving.