I would, because i would think of you: the other monsters. There are a LOT of monsters in the world who really need such a godess like Gaga. The number of monsters are more than me and the little group who would miss me.... so it would be fair to save her even in sake of my life. Plus than somehow i would live inside her forever.
There is absolutely nothing i wouldnt do for her, take a bullet, give a kidney, id even let them put her brain in my body just so she could live longer