Although distributed fiber-optic sensing of axial strain and temperature is a well-established technique, there are almost no demonstrations of distributed hydrostatic pressure sensing. The main obstacle for such measurements is the low sensitivity to pressure of standard optical fibers. Structured fibers, such as photonic crystal fibers can be made pressure-sensitive by means of an optimized arrangement of their internal microstructure. In this paper, we demonstrate - for the first time to our knowledge - distributed birefringence and hydrostatic pressure measurements based on phase sensitive optical time-domain reflectometry (OTDR) in highly birefringent photonic crystal fibers. We study the response to hydrostatic pressure of two dedicated pressure-sensitive photonic crystal fibers in the range from ∼0.8 bar to ∼67 bar with a 5 cm spatial resolution using a phase-OTDR approach. We find differential pressure sensitivities between the slow and fast polarization axes of the studied fibers of -219 MHz/bar and -95.4 MHz/bar. These values are ∼3.8 to ∼8.8 times larger than those demonstrated previously in distributed pressure measurements with other photonic crystal fibers.