Acting at high speed enables creatures to survive in their harsh natural environments. They developed strategies for fast actuation that inspire technological embodiments like soft robots. Here, we demonstrate a series of simulation-guided lightweight, durable, untethered, small-scale soft-bodied robots that perform large-degree deformations at high frequencies up to 100 Hz, are driven at very low magnetic fields down to 0.5 mT and exhibit a specific energy density of 10.8 kJ m−3 mT−1. Unforeseen asynchronous strongly nonlinear cross-clapping behavior of our robots is observed in experiments and analyzed by simulation, breaking ground for future designs of soft-bodied robots. Our robots walk, swim, levitate, transport cargo, squeeze into a vessel smaller than their dimensions and can momentarily close around a living fly. Such ultrafast soft robots can rapidly adapt to varying environmental conditions, inspire biomedical applications in confined environments, and serve as model systems to develop complex movements inspired by nature.