I do not think there is a solid 100% answer to that question. A monster should be something different from a human, but simply defining this in matters of appearance or power is difficult, if not impossible.
When I am looking for a monster for Pia to encounter, I want someone who can leave her awed, thrilled or terrified (or all of the above). There must also be some sort of feeling of danger, but it does not have to be obvious. And the chance to experience good sex, obviously
I guess that can be done with appearance, what powers it yield or they way it acts (or a combination of the above).If I was presented with basically a human boy with a couple of random powers or traits , I would probably not be too keen. All due respect to Twillight fans, but I do not see Edward taking Pia on a rollercoaster ride of terror and forbidden lust.
To be honest, I think my own monster, the pixies, is actually stretching it. I was very unsure when I got the idea, that is why I aired it in the Roleplay Discussions area before writing the actual profile, I was quite aware that this might not be something people would approve off. I think they work mainly because there is absolutely no chance they would ever pass as a human, and they are 100% amoral.
I'd still like to try something different one day, perhaps something more clearly alien, perhaps something adapted to space, the labs or the basement.