Jet Boots are arguably the most unique weapon in the game as far as gameplay goes. They are the only Tech weapon in the game that has Photon Arts. Said Photon Arts are the only ones that scale with TATK by default, yet are considered Striking based. Jet Boots are also the only weapons that can double jump and change their element. To top it off, they have the most elaborate set of Shift button actions in the game.
This part will do its best to explain how all of that is supposed to work.