We report the barocaloric performance of cadmium-dicyanamide perovskite [(CH3CH2CH2)4N]Cd[N(CN)2]3 ([TPrA]Cd[dca]3). The introduction of Cd, a large second-row post-transition metal, into this hybrid organic-inorganic perovskite structure leads to three separate thermally driven phase transitions and four polymorphs, which we characterize in full using temperature-dependent X-ray diffraction and temperature-dependent calorimetry. Amongst these transitions, the non-isochoric orthorhombic to tetragonal phase transition at high temperatures, with a large volume change of ∼0.4%, leads to a large reversible pressure-driven isothermal change in entropy of ∼11.5 J K-1 kg-1, and a giant barocaloric tunability of the transition temperature with pressure of ∼38.2 K kbar-1, which are both desirable for future low-pressure barocaloric cooling applications.