The main key is that you need to stock up on a massive number of Power Rush badges, which you can only do after completing Frankie's trouble centre sidequest, which requires beating Chapter 6 first. You then need to Chet Rippo (Rogueport sewer area directly below Frankly's house, then go in the pipe that requires Bobbery) and use him to lower Mario's HP to 5 so that he is permanently in Danger. This means your power rush badges are activated, which gives you +2 attack power for each one you equip, and each one only costs 1BP to equip. This makes you insanely powerful, e.g. if you equip 20 power rushes, you get 43 attack power (before Power Lift or power boosting items), meaning you can flatten anything other than the final boss and some of the superbosses with a regular jump attack.
Other badges/items you're going to want to have equipped:
Multibounce (so you can take out any wave of regular enemy attacks, or bosses that have additional targets such as Magnus' fists)
Life Shrooms (in case you mess up)
Chill Out (so you don't die to a first strike; remember Mario is vulnerable at 5HP)
Power Bounce (so you can take out particularly tanky foes)
Spike Shield and Ice Power (so you don't need to worry about spikes or ice interfering with multibounce/power bounce)
Flower Saver (so that Multibounce costs only 1FP)
(Optional) FP Drain so that you get the 1FP back from multibouncing at the cost of dealing 1 less damage (which can easily be compensated by adding another Power Rush), particularly useful if you don't have a high FP limit and you're doing a lot of battles back to back, such as in the Pit
(Optional) Add a bunch of Last Stands and/or Close Calls (which like Power Rush, are permanently active if Mario's max HP is 5), so that if Mario does somehow get hit, the attack will likely miss and/or deal less damage, so you don't waste a Life Shroom.
Other badges/items you're going to want to have equipped: