We report a pressure study of the metamagnetic/ferroelectric hybrid heterostructure of a quenched FeRh thin film (25 nm) grown on single crystal barium titanate (BTO). It has been previously reported that when the BTO undergoes a crystal transition a massive magnetization and coercivity change is triggered in the highly strain sensitive quenched FeRh thin film. Therefore quenched FeRh makes for an ideal probe for mapping a materials structural phase transitions. In this work we demonstrate this effect as a function of both temperature and hydrostatic pressure. As a result, we present the pressure dependence of the hybrid material which aligns identically with the BTO substrates pressure dependence reported in literature. The concept of combining a structural phase transitional (SPT) material with a magnetostrictive magnetic metal has been shown with vanadium oxides and our findings here prove that this methodology can be extended to strain sensitive metamagnetic materials systems in thin film, and possibly in bulk, heterostructures.