Extending single attosecond pulse technology from currently sub-200 eV to the so called 'water window' spectral range may enable for the first time the unique investigation of ultrafast electronic processes within the core states of bio-molecules as proteins or other organic materials. Aperiodic multilayer mirrors serve as key components to shape these attosecond pulses with a high degree of freedom and enable tailored short pulse pump-probe experiments. Here, we report on chirped CrSc multilayer mirrors, fabricated by ion beam deposition with sub-angstrom precision, designed for attosecond pulse shaping in the 'water window' spectral range.