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On the title screen, hold down Shoot+Jump until you hear a tone. That activates the special mode for Hadoken and Sei'ei Enbu (sometimes incorrectly called Genei Jin). The mode grants Mega Man two special abilities.
The first is the 'classic' Hadoken. While using the Mega Buster, input down > down-towards > towards + Shoot to throw a Hadoken with an actual Hadoken-throwing animation rather than just shooting it from your arm.
Sei'ei Enbu is the cloning Super Art/Combo used by Yang in Street Fighter 3 and 4. Genei Jin is the Super Art of Yang's brother Yun, which looks similar in execution but operates differently, increasing juggle potential rather than actually granting cloned attacks To activate Sei'ei Enbu, push Shoot + Weapon Switch Right at the same time with the Mega Buster selected. This creates two shadows that will follow Mega Man around. He will be able to run faster and jump a bit higher, and one of the clones will also shoot after he does as well, doubling your firepower. The extra shots are of limited use against bosses because of the invulnerability period they have after being hit, but it works great against normal enemies, especially when you stack multiple charge shots.
Sei'ei Enbu can only be activated after doing the Shoot+Jump code on the main menu, which the Cheats section here doesn't specify. That's probably the problem you're having. If you don't see a weapon meter while using the plain Mega Buster, then you didn't input that original code and can't access the Hadoken or Sei'ei Enbu.