No More Heroes 3 is a unusual game, and that extends to how you save your progress. The game doesn’t have an autosave function, so make sure you save often so you don’t lose any of your items, currency, or progress.
To save your game, you need to visit the toilet. There is one in your hideout, but others can be found all over the map. They won’t automatically be available, however, and because this is a Suda51 game, there will be some work to be done to unlock them.
You will actually need to repair the toilet to be able to use it, and this means unclogging it. This involves a mini-game that you will need to complete. You will need to use the left stick to position a plunger and when it flashes red and says “Here”, you will then need to either shake the Joy-Con or push the right stick forward and backward to work on the clog.
You will need to go through a few different positions to fully unclog the toilet, after which point Travis will be able to use it and save the game. The good news is that you only need to do this once for each toilet, but you will want to make sure you do it for each one you find so you always have a convenient way to save the game.