In order to battle with dragons in the wormhole, we have to lead our brigade or fleet to join an existed corps. A good strategy is to join a corps with your best brigade or fleet. If there is no corps you want to join, you can create your own corps.
When the battle you joined starts, you can join the battle.
You can launch an attack using your brigades or fleets.
When the battle ends, you can claim your rewards in the history.