Perfect absorption in wave transmission problems is achieved by subwavelength resonant scatterers realizing critical coupling conditions, when all eigenvalues of the scattering matrix relating the propagating incoming and outgoing waves vanish simultaneously. While this concept has been extensively explored in electromagnetics and acoustics, its extension to flexural waves remains challenging, as conventional transverse resonators typically provide only a single monopolar resonance, fundamentally limiting absorption in transmission problems to 0.5. In this work, we overcome this limitation by introducing point-like scatterers with two resonances, combining transverse (monopolar) and rotational (dipolar) responses within a single structure. An analytical framework relating the scattering coefficients to the polarizability of the scatterer is developed, from which the impedance conditions for perfect absorption are derived. Bidirectional perfect absorption is achieved using mirror-symmetric scatterers with diagonal polarizability, whereas unidirectional perfect absorption is achieved through non-mirror-symmetric scatterers by exploiting hybrid monopolar-dipolar resonances, which induce Willis coupling and non-diagonal polarizability. The proposed concepts are validated experimentally, showing close agreement with theory and absorption above 0.99 for both configurations. These results open new possibilities for elastic-wave control using compact multi-resonant absorbers.