To get onto a certain characters route in Period Cube, you need to select certain ways of dealing with the monsters you meet and say certain things.
Here is a guide to get onto all of the character’s routes:
Astrum: Run, Dodge, Harp
Zain: Run, Use Knife, Run or Crouch down, Run, Run
Hiroya: Knife, Knife, Say “Don’t attack Hiroya”
Libera: Knife, Knife, Say “I think this person is right”
Radius: Knife, run, use harp
Demento: Get onto Astrum’s route, keep affection with him low (I’m not sure that matters), In Chapter 5, say “You’ve already finished it” when you deal with Demento, in battle increase ally strength, then choose “Demento, stop!”
Poyo-poyo: Finish Hiroya’s and Libera’s routes, then Poyo-Poyo’s route will unlock. Use knife, use knife, and then a third option will appear when Hiroya and Libera are arguing. Do not agree with either of them. I recommend you save this route for the end.