Extremely Red Red Eye

From ANN:

The manga is set in a Japan that has been under constant threat of giant monster attacks for a number of years, with giant heroes employed by the monster defense agency Midas only barely holding off the attacks. The story centers on Aki, a one-legged girl who moves to the new seaside capital Isora after she is saved by the strongest hero Red Eye. She has an unfortunate encounter with a mysterious boy named Gaito, and later finds out that he is in fact her long-admired hero Red Eye.