Non-Hermitian systems, distinguished by the presence of exceptional points and non-Hermitian topological states, have transformed sensing technologies through the implementation of novel physical mechanisms. However, despite their demonstrated potential, existing non-Hermitian sensors are predominantly limited to static operational configurations, which substantially restricts their effects in detecting time-varying signals. Here, we transcend this limitation by introducing a new sensing framework: non-Hermitian Floquet topological sensors (NHFTSs). This approach harnesses the synergistic interplay among time-periodic driving, nonlinear dynamics, and non-Hermitian topology to enable ultrasensitive detection of dynamic signals. NHFTSs establish nonlinear non-Hermitian Floquet topological zero modes as robust global attractors. These modes manifest extraordinary sensitivity to dynamic boundary perturbations, exhibiting frequency shifts that scale exponentially with system size. Moreover, NHFTSs possess exceptional resilience against both background noise and structural perturbations, a feature enabled by the dual protective mechanisms of nonlinear stability and topological band gaps. Notably, the signal-to-noise ratio of NHFTSs can be exponentially amplified through sensor size scaling. We experimentally validate the NHFTS using time-varying topolectrical circuits, demonstrating their unparalleled capability in detecting dynamic electrical signals with high sensitivity and signal-to-noise ratios. This Letter not only establishes a new paradigm for non-Hermitian dynamical sensing but also paves the way for exploring non-Hermitian topological phenomena in Floquet nonlinear systems, with profound implications for the development of next-generation non-Hermitian sensors and beyond.