Are these cores from the Anime?
I don't remember them being in the games at all.
My plan for Zygarde is that the MC will chase her when she's in 10% Dog form, 5 of the dogs will fuse into her 50% Snake form where she'll fight you, then she'll fuse again into the 100% Knight form for another fight.
After that she'll usually stay in 50% Snake form with her other Zygarde Cells all stored in her room.