To battle the Club Boss, you must first join a club! You can find a club to join by tapping on the "Clubs" icon at the bottom-right of your screen.
Once you've joined a Club, tap on the "Hawkins" button on the bottom-left of your screen, and then tap the "Club Boss" button.
When you tap the "Club Boss" button you'll be taken to a screen with the "ENTER" button at the bottom. To start a battle, tap this button. You'll then be prompted to choose the characters you'd like to use in battle.
You'll have 90 seconds to do as much damage to the Club Boss as you can. The battle will end once the 90 seconds are over or all of your characters have been defeated (whichever event occurs first.)
If you Flee in a Club Boss Battle, one of your attempts will be consumed, and the Boss takes the amount of damage your team has done up until the point of fleeing the battle.
If your Club defeats their Club Boss, the Club Boss Level will increase for the next day. Similarly, if the Club does not manage to defeat the Club Boss, its level will decrease.