A broadband reflection mirror that can realize maximum uniform reflectivity is an important optical element in the water window region. In this paper, a stacked multilayer mirror with optimized structure for achieving broadband reflection in the water window region is presented. A genetic algorithm with a two-parametric merit function is employed to achieve maximum uniform reflection in the desired spectral band. 4.90% average reflectivity with 0.25% root-mean-square deviation in the range of 370-390 eV is achieved by a Cr/Sc stacked multilayer with 40 periodic multilayer structures. Compared with aperiodic multilayers, proposed stacked multilayers exhibit better optimization efficiency, design robustness, and thickness error tolerance. This research provides an efficient method for designing broadband reflection mirrors in the water window region, and may be helpful for steering broadband water window sources, such as high order harmonics and attosecond pulse.