Blue treasure chest

[joker_mausland]

Is there any way to open them? Every one I see is always locked.

[Kizyr]

You have to defeat all enemies on the screen in Virtue Mode first. Once all the enemies are cleared, you can open the blue chests. It says this in the instruction manual somewhere. KF

[Alunissage]

Also, you can keep track of how many enemies you have to go in the subscreen -- there are boxes that get checked off once you defeat another one. You do have to defeat them in a certain time (a minute, I think), which is indicated by the clock -- once the time runs down a previously defeated monster will reappear. The clock is reset after each battle.