The problem is this: We are stuck between having Dr. Eggman use eggmobile, which is a motif that is already taken, potentially limiting the excitement, giant-style trepidation factor, copious number of options, and power his moveset could have if he used a selection of his mechs across different moves ;and forcing Eggman to fight on foot, and he is famous for not being able to do that.
So my proposition circumvents all of that: Eggman starts on foot, like everyone else. And he is at a major deficit. He has no attacks, and cannot dodge or grab. Basic stats are of the egg-custard-everyday-for-breakfast-lunch-and-dinner kind. Where he lacks ( no... disgraces himself ) in the hand-to-hand or foot-to-land department, he makes up for by being able to fly off the screen momentarily with eggmobile using his specials, only to return with a giant, flinch resistant machine, which would include egg hawk, etc. depending on the directional input. The object is then to damage the machine enough so it explodes and launches Eggman, or attack the cockpit for more damage to force Eggman to eject with shield input, in which case he cannot spawn that machine or any other again for the stock, and can reenter at any time.
I know that is a bit much, but I want him to have as many options as possible.