Analog method for measuring distinct phase shifts
If you had a reference at the same frequency, let's say an unpredictable VCO driving two paths, one direct, the other through a 90 degree phase shift device, then the two signals could be compared in a simple phase detector. Each change of 90 degrees would result in a change of output.
If you only have one signal, then an unpredictable frequency means an unpredictable rate of change of phase. You want to detect a sudden 90 degree phase shift. You had better hope that there's some way of distinguishing the unpredictable wander from the 90 degree shifts, perhaps the frequency varies slowly enough for a PLL to track it? If so, monitor the error signal at the phase detector of the PLL. Most of the time it will wander up and down a bit to track the slowly varying frequency. From time to time, it will jump by 90 degrees. Choose the loop bandwidth to be fast enough to track the unpredictable variations in frequency with little phase error at the PSD.