Is the achivement "The tale of Argos and Io" and "Cthonic Regalia" have requirement? It seems they just accomplish within the main story.
Yes, some achievements are obtained as part of the game's normal story progression. This way the achievements screen serves as an easy way to check how far someone got in the game in their most advanced playthrough.
What is the star on Asterion head means?
I'll leave that to interpretation! :)