From the Super Mario Wiki
Bowser and...Bowser? is a post-game level in the Bowser Jr.'s Journey mode of Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey.
After hearing about Bowser Jr.'s adventure from Ludwig von Koopa, Bowser invites his son over and personally challenges him to a duel so he can prove himself once and for all. The duel itself consists of five battles with various enemies, most of which are unique to each battle; Bowser himself acts as the the enemy captain for the fourth and fifth battles. In the fourth battle, he acts as a Ranged-type unit with the Special Skill Piercing Projectile; during the fifth, he is a Melee-type unit with the Special Skill Spin to Win.
After the battles are completed, Bowser declares that Jr. is "even" with him now that he's proved his growth, but then they both resume fighting, and continue for two weeks straight before stopping completely. After finally stopping their fight, both of them realize that their chaotic fighting undid the repairs made to the castle. Bowser then joins the team.