Is there a phase shift $pi$ radians when a pressure wave is reflected upon a medium having less acoustic impedance?

Short answer: Yes, for a pressure wave reflected from a surface with less acoustic impedance than the original medium the phase shift would be $pi$ radians, neglecting absorptive processes.

Longer answer:

I have some equations, so let me provide the full context. Consider a plane pressure wave propagating in a homogeneous fluid and is normally incident upon a flat interface to another domain. Let the characteristic acoustic impedance of the original domain be denoted as $Z_1$ and for the second domain as $Z_2$. The reflection coefficient may then be written as $$ R = frac{Z_2-Z_1}{Z_2+Z_1}. $$ In general $Z_1$ and $Z_2$ may be complex quantities (frequency domain; they would be convolution operations in the time domain), but if we neglect absorptive processes they are real. Thus, for $Z_2>Z_1$ (e.g., rigid surface) the reflection coefficient is positive, and the phase change is 0 radians. If $Z_2<Z_1$ the reflection coefficient is negative, which is a phase change of $pi$ radians. Obviously, complex impedances lead to reflection coefficients that are not restricted to 0 or $pi$ radians phase shifts, and in general are not those simple cases.