The Skullman's personality is portrayed at least three different way during the course of these ninety pages. When he's first introduced, he's portrayed as somebody who's very flippant about killing others. He has the power to hypnotize people and supposedly he could use this power to prevent people from fighting back or being threats, but he chooses to kill them instead. At this point in the story, even the murders are drawn in an almost slapstick comedy style, reinforcing the idea that killing means nothing much to him. This first portrayal of his personality also matches how the police perceive him: bloodthirsty and enjoying killing.
As the story reaches its climax, the murders become less slapstick and have more gravitas to them. I see this as preparing the reader for the second portrayal of the Skullman's personality. Instead of shooting people willy-nilly, his killings are portrayed as having a motivation behind them. Of course, this motivation is retroactively applied to all of his previous murders as well. He sees his parents' killer as influencing society and culture from the shadows and causing people to live corrupted lives. He sees himself as the arbiter of justice and seems to judge everyone else as being unrighteous. Of course, this is nothing more than a hypocritical, self-serving justification he tells himself so he doesn't have to feel bad for killing people...and enjoying it.
At this point in the story, we find him stroking his own ego, condemning others for the minutia of their sins, and caught up in his own self-righteousness saying that he'd even be willing to kill everybody in Japan. But then the story shifts and he learns some people he had trusted seemingly had wanted the extinction of humanity itself. As soon as he heard that, he called them monsters and was devastated to the point of weeping. I consider this the third portrayal of his personality because it's the first time we see him being capable of caring for others. The author chose to portray him as being empathetic and capable of recognizing the evil of genocide, though of course he only recognizes the evil when its somebody else desiring mass murder--when he himself desires it, it's justified.
I think the author was trying to have the character gain depth and become more relatable by having him change from a brutal monster to a homesick teenager. The problem is that making a sociopath a relatable character takes time and nuance and this story had neither of those. So whenever it got to the point in the story when the audience is supposed to feel conflicted about whether to empathize with the Skullman or not, I was just asking myself "Why does he now have a completely different personality?"