A Boss Battle is a battle in game, where the player has to face off against a Boss.
An example would be, for example, if a there is a corrupt teacher in a school, and the player is required to stop the teacher, in game, there could be call for a Boss Battle.
However, here's something to keep in mind:
It would be wise not to toss in a Boss Battle right away, not until there's been some fighting experience with some of the subordinates, first.