We report on a synthesis protocol, experimental characterization, and theoretical modeling of active pulsatile Belousov-Zhabotinsky (BZ) hydrogels. Our two-step synthesis technique allows independent optimization of the geometry, the chemical, and the mechanical properties of BZ gels. We identify the role of the surrounding medium chemistry and gel radius for the occurrence of BZ gel oscillations, quantified by the Damko''hler number, which is the ratio of chemical reaction to diffusion rates. Tuning the BZ gel size to maximize its chemomechanical oscillation amplitude, we find that its oscillatory strain amplitude is limited by the time scale of gel swelling relative to the chemical oscillation period. Our experimental findings are in good agreement with a Vanag-Epstein model of BZ chemistry and a Tanaka Fillmore theory of gel swelling dynamics.