Pushing the brightness limit of electron sources requires simultaneously minimizing the intrinsic emittance and maximizing the accelerating field. Alkali-antimonide photocathodes exhibit excellent properties at low fields, yet their high-field photoemission physics remains poorly understood owing to acute vacuum sensitivity. Here, we demonstrate robust photoemission from alkali-antimonide photocathodes in a radio-frequency gun at peak fields exceeding 100 MV/m, with quantum efficiency maintained above 1% for more than two weeks, enabling the first systematic measurements of their high-field brightness limits. The measured field dependence of the intrinsic emittance provides direct insight into photoemission physics at high fields. Near-threshold photoemission further reduces the intrinsic emittance, increasing the attainable brightness, and reveals constraints imposed by surface roughness. This work opens the high-field regime for advanced photocathodes, extending the brightness limits of electron sources.