In quantum metrology, entanglement represents a valuable resource that can be used to overcome the Standard Quantum Limit (SQL) that bounds the precision of sensors that operate with independent particles. Measurements beyond the SQL are typically enabled by relatively simple entangled states (squeezed states with Gaussian probability distributions), where quantum noise is redistributed between different quadratures. However, due to both fundamental limitations and the finite measurement resolution achieved in practice, sensors based on squeezed states typically operate far from the true fundamental limit of quantum metrology, the Heisenberg Limit. Here, by implementing an effective time-reversal protocol through a controlled sign change in an optically engineered many-body Hamiltonian, we demonstrate atomicsensor performance with non-Gaussian states beyond the limitations of spin 1