Phase modulation plays a crucial role in shaping optical fields and physical optics. However, traditional phase modulation techniques are highly dependent on angles and wavelengths, limiting their applicability in smart optical systems. Here, we propose a first-principle theory for achieving constant phase modulation independent of incident angle and wavelength. By utilizing a hyperbolic metamaterial and engineering-specific optical parameters, different reflective phase jumps are achieved and tailored for both transverse electric (TE) and transverse magnetic (TM) waves. The aimed reflection phase difference between TE and TM waves can be thus achieved omnidirectionally and achromatically. As an example, we propose a perfect omnidirectional broadband reflection quarter wave plate. This work provides fundamental insights into manipulating optical phases through optical parameter engineering.