This paper proposes phase-shift-amplified optical fiber interferometry based on microwave photonics (MWP) for sensing applications with substantially-improved sensitivity. The principal idea of the system combines a destructive interference-based phase-shift amplification technique with optical carrier-based microwave interferometry (OCMI). The phase sensitivity of the OCMI system is significantly improved due to the phase amplifier, and more importantly, can be adjusted by simply varying the amplitude ratio of the two beams used in the interferometer. The amplification of the phase sensitivity is numerically investigated and experimentally demonstrated using a Mach-Zehnder interferometer for temperature and strain measurements. The measurement results accurately match theoretical predictions. Moreover, we demonstrate that light-scattering dots in the optical fiber core, created by tightly-focused femtosecond laser pulses, can be used to precisely tune the amplitude ratio of the two-beam interferometer. We postulate that amplification of several orders of magnitude in phase sensitivity can be achieved in the OCMI system by employing micromachining methods.