Here is the full list of all 10 Sky Battles achievements.
Took down bomber and collected 15 gems
Destroyed sea monster and collected 10 gems
Conquered the Kraken and collected 10 gems
Owned two trolls and collected 15 gems
Defeated an airship and collected 15 gems
Conquered two fire breathing dragons and collected 15 gems
Collected 15 gems in the corridor and lived to tell about it
Destroy the leaping cyclops and collected 15 gems
Destroyed the giant robot and collected 10 gems
Collected 20 gems and survived cave obstacles