NEED HELP ON PARENT THE MODEL

Hi,

I have an issue for parenting the model. I am making this frog helmet and want it to stay as its shape. I parent the helmet with the bone it stays it shape but it doesn't go along with the character's movement. And I change to parent the helmet to armature with auto weight. The helmet deforms its shape but able to go along with the character. Please advise if I can fix that. (Note I already weight painted) BELOW VIDEO SHOWING THE ISSUE: Many Thanks!