As you play through the Main Story of Yakuza 6, you will be faced with a number of Boss Battles. These are battles against some of the main characters Kiryu will cross paths with during the story itself, and these characters are usually much stronger than the thugs you will throw down with on the streets. (Some of them will even use weapons against you.) Unlike some other games, you will actually face a number of Bosses in a number of different battles. Honestly, you should expect to face at least one Boss per Chapter found within the Main Story.
If you are looking to defeat said Boss Battles with ease, there are a number of things you can do to better improve your odds. The first is to boost your Stats was you gain EXP throughout the Main Story, making Kiryu all the stronger both when dealing attacks and withstand them as well. Another thing you can do is save your Heat Gauge for these battles, allowing you to use Extreme Heat Mode multiple times in order to deal massive damage to these Bosses. This isn't the best technique since you will probably need your Heat Gauge for other fights, but if you don't mind waiting, it can pay off in dividends. Finally, during most Boss Battles, you will have a sequence or two where you must quickly click the Button the screen informs you to press. Make sure your reaction time is swift, as you don't want to be on the receiving end of some of these blows.