We investigate the problem of reconfigurable intelligent surface (RIS)-aided monostatic sensing of multiple mobile targets under line-of-sight (LoS) blockage using a dual-functional radar-communications base station. For the purpose of target detection and delay/Doppler/angle estimation, we derive a detector based on the generalized likelihood ratio test (GLRT), which entails a high-dimensional parameter search with high complexity due to angle-Doppler coupling. To circumvent the coupling effect, we introduce a repetitive RIS phase profile design accompanied by a multi-target detection/estimation algorithm based on orthogonal matching pursuit where each iteration solves the single-target GLRT problem and outputs the corresponding parameter estimates. Moreover, as a low-complexity alternative, we introduce a novel subspace-based algorithm based on twodimensional unitary ESPRIT to retrieve target parameters in a non-iterative manner. Simulation results verify the effectiveness of the proposed algorithms, demonstrating their convergence to theoretical bounds and revealing significant improvements over state-of-the-art benchmarks in complexity and performance.