Asadora!

"A deadly typhoon, a mysterious creature and a girl who won't quit." --Provided by publisher. "Asadora! tells the story of Asa Asada's life, starting in post-war Japan, and spanning into the then-present year 2020, when a large monster rampages through Tokyo. The story begins in 1959 when Asa looks for a doctor for her mother in labor, only for her to run into a burglar and held for ransom. When Typhoon Vera hits Japan, Asa and her kidnapper must work together to survive." -- Wikipedia