It is more like Sigma can possess the whole building and use them to his advantage. And as long as his core stays intact, he won't take much damage.

His armor pretty much protect him against anything. His weak spots have elemental defense, and large attack (such as some whole screen attack) won't be effective because it would require skillful and precise aiming in order to deal out effective damage. (As mentioned, small things like X-Buster, or close ranged melee.)

Sigma has a dog, Velguader. An agile beast (well, mechanical beast) which can breath out fire and ice.

The assumption of one can fly and therefore he can dodge everything isn't very good. Because Sigma can teleport.

Being a confidence maverick, I would believe that Sigma won't hesitate to attack, and then he will find Seymour's weaknesses and analyze his opponents' moves.