Screw the Apocalypse! My Daughter's Gonna Die! [Post-Apocalyptic Progression Fantasy]

They told me to save the world. I told them to buzz off! Believe me, I had bigger problems than fixing a world filled with man-eating zombies and radioactive beasts. I mean, what kind of father would I be if I put the world over my beloved daughter, Sunshine? Unfortunately for her, she was infected with this rare disease from the after effects of the nuclear bomb that hit my home of New York and the only way to save her was to break through the limitations of this new Earth in order to find her a cure. And I had to hurry or else she'd be dead by the end of the year. Well, it can't be too hard, right? Especially with this new form I got after getting eaten by a couple zombies that allow me to use the powers of a "really cool, nuclear energy blasting, terrifying monster!" At least, that's what my daughter calls it! Schedule!?: Daily for the first month then 3x a week!  Chapters usually posted in the Evening (EST Timezone, Th, F, and S) What to Expect!?: Some good-ole fashioned Father-Daughter duo moments!  Strong to Stronger Protagonist  If you're a fan of ANY Anime/Manga Battle Shounen (such as Naruto, HxH, or Dragon Ball) this is the story for you! 1.5k-2.5k word chapters!  Gradual Power Progression of both the MC and his Daughter! Character Development! (Most characters will have flaws they’ll grow out of) 95% Main POV 5% Other POVs Mysteries and Foreshadowing (Don't read this story expecting all the answers immediately) NOTICE: The first four chapters are all rewrites, so a few of the beginning chapters might not mesh well with them. Expect them to be rewritten in the future. Also expect a lot of “.5” chapters to be added too, so don’t be too confused on where certain parts end. Expect them all to be finished and properly ordered when I finish this first saga of the story.