Lattice compression has emerged as a fundamental tuning parameter for nickelate superconductivity. Pressure acts as a trigger to induce superconductivity in bulk Ruddlesden-Popper nickelates. For infinite-layer nickelate thin films, compressive epitaxial strain and rare-earth ion chemical pressure have been used to substantially enhance the superconducting transition temperature (T_c). Efforts to go further have been constrained by the limits of epitaxial stability or the challenges of measuring thin films in high-pressure environments. Here, we overcome this limitation by developing a technique to incorporate freestanding infinite-layer Nd_(0.85)Sr_(0.15)NiO₂ membranes into a diamond anvil cell. Using this platform, we observe a strong increase in T_c up to our highest measurement pressure of ∼90 GPa, where a superconducting downturn can be observed near liquid nitrogen temperatures. Strikingly, we find a simple linear enhancement of T_c at a rate of 0.65 K GPa⁻¹, with no signs of saturation. This suggests that the pairing strength in infinite-layer nickelates can be raised to a surprisingly high scale, using an approach that can be broadly applied to many two-dimensional materials.