So you get the star badge on your save file after 225 levels, but there are also 6 secret levels that bring the total to 231, but don't count for the badge.

Do you only need what the game considers "complete", or do you really need to beat all levels? I feel that this should be specified in the rules.

I don't have a capture card for Nintendo Switch, but I can use a homebrew called SysDVR to stream video output to a PC. Would this be allowed for speedrunning, or should I just record the screen instead?

https://github.com/exelix11/SysDVR

At the start of the boss fight, make the boss bigger and then if you grow the first fireball quickly enough, it will hit him and skip straight to the bombs.

Demonstration (at 13:28)