Paper Mario The Thousand Year Door: Prince Mush Superboss Battle

This battle with Prince Mush is a new addition to the game in the HD rerelease on the Switch. It can be unlocked by completing Chapter 4 and becoming champion in the Glitz Pit for a second time. Prince Mush will send you an email challenging you to a battle. I immediately attempted the battle as soon as it became available here.
This is a difficult fight as Prince Mush has very high defence and can do significant damage after charging up. Prince Mush changes battle stances from a vertical hop (vulnerable to jumps), and side to side hops (vulnerable to hammers). He will completely dodge attacks that he is not vulnerable to from his stances. After his HP gets low enough (below 40 I think), he switches to his final stance where he is completely invulnerable to all forms of damage. He can also create fake copies of himself to make it harder to hit him, but he never had the chance here. The only way to break this stance is to perform a superguard on one of his attacks. This will drop his defence to 0 and allow you to damage him for a single turn.
My strategy here revolved around finishing the fight as quickly as possible, so I equipped as many badges as possible to boost damage and defence. I used the Hammerman badge (lose ability to jump in exchange for +1 damage) as hammer abilities are particularly useful for the battle. Piercing blow allows you to bypass his high defence in the first half of the battle, while Power Smash is great for a strong hit after a superguard. Quake Hammer is a great move to get rid of any copies he makes as well.
Upon completing the battle you get 30 coins of fight money from the pit as well as Prince Mush's belt if you go and talk to him afterwards. The belt is a key item and does absolutely nothing except give you bragging rights.