Super Mario Bros. 2 is the infamous sequel to Super Mario Bros. that was released only in Japan for the Famicom Disk System. Considered too difficult and too similar to the original game, it was skipped over for localization in favor of making Doki Doki Panic into the actual Super Mario Bros. 2 for the NES. This game would later be remade in Super Mario All-Stars as Super Mario Bros: The Lost Levels.
In this run, JQJ decides to complete every level in the game using Luigi, including Worlds 9, A, B, C, and D, which are usually unlocked after completing the game multiple times. This run begins after having fulfilled the requirements for unlocking Worlds A to D. As Luigi controls differently from Mario, certain strategies had to be adjusted. For further details, you can read the author's notes here.