"To defeat the boss" means to successfully overcome and win against a person in a position of power or authority, typically in a competition or challenge. Full definition
These challenges are available after defeating the boss in each of the four regions and learning the special technique to reach the secret areas inside of each world. (miketendo64.com)
After defeating the boss of each world, players can move on to the next, culminating in the final fight in the last world. (superluigibros.com)
The actual fight with the boss wasn't any easier, but I felt like a failure became Dark Souls II decided I wasn't capable of defeating the boss without help. (bitcultures.com)