Mr. A is a Parasite who sees Shinichi as a threat. He's not particularly bright—Reiko openly calls him a fool, and even Migi dismisses him as "not one of our smart ones." What he lacks in cunning, he makes up for in recklessness. Mr. A has zero interest in subtlety or playing human; he'll shapeshift openly in public without hesitation, figuring he can always punch his way out of trouble, run, and just grab a new face. It's the kind of thinking that defines him.
He's also the biological father of Reiko's child, though that's almost beside the point given how little they seem to have in common.
Things come to a head when Mr. A tracks Shinichi down to his school with murder on his mind. Shinichi and Migi manage to inflict serious damage during the fight, but they're forced to cut and run before they can finish him off.
Content compiled by AnimeList.moe from publicly available sources.