Boss Battles are the way to advance to different areas in the City and map. You have to beat the Area Boss to move to the next city.
To access the fight and Unlock the next part of the map, walk into the area and a pop-up will display the Cash needed to continue.
When you pay to unlock the battle, you gain access to the ring to fight that Area boss. All Battles last 1 minute, with the Boss having to be defeated between that timeframe. Avoid red areas of attack in order to fight more effectively.
As you advance to different areas you will need stronger Powers to defeat the Boss.
You can leave the fight at any time by entering the Flee the battle vortex.
If you are unable to defeat the Boss, you can enter the ring as many times as needed to defeat him.
Once you beat the Boss, you will receive rewards and be able to exit back to the map via the Exit vortex.