Microgels are elastic and deformable particles with a hybrid nature between that of polymers and colloids and unconventional behaviors with respect to hard colloids. We investigated the dynamics of a soft microgel made of interpenetrated polymer networks of PNIPAM and PAAc by means of coherent X-ray and light scattering techniques. By varying the particle softness through the PAAc content, we can tune at wish the fragility of IPN microgels. Interestingly, we find the occurrence of a dynamical crossover at a critical weight concentration, which leads to an evolution of the structural relaxation time from a super-Arrhenius to a slower than Arrhenius behavior, a minimum for the shape parameter of intensity autocorrelation function, and the emerging of distinct anomalous mechanisms for particle motion. This complex phenomenology can be described by a Fickian diffusion at very low concentrations, an effective non-Fickian anomalous diffusion at intermediate values, and a ballistic motion well described within the mode coupling theory.