Sonic Crystal Noise Barriers (SCNB) based on Sonic Crystals (SC) with Helmholtz Resonators (HR) can provide additional insulation bands beyond the Bragg bandgap (Bragg-BG). Yet adding HR does not always increase attenuation. The interaction between Bragg-BG and the local-resonance bandgap (HR-BG) is strongly governed by the relative position of the local resonance with respect to Bragg, (fHR versus fBragg), and by the alignment of the resonator necks with the incident wave (0° and 90°). This work investigates a dual-regime SCNB built from multiresonant asymmetric scatterers. Each scatterer integrates two orthogonal HR with coupled cavities. The acoustic response is obtained using 2D FEM models. Both periodic analyses (band structure) and finite arrangements (transmission) are considered. The focus is the Insertion Loss (IL) in the 500–2500 Hz range. Analytical tuning is hindered by the irregular cavity geometry. Therefore, a multiobjective optimisation is employed to adjust geometric parameters. The aim is to place the relevant attenuation ranges and make them complementary for the two orthogonal orientations. Experimental validation is performed on a 3D-printed prototype. Measurements are carried out in an anechoic chamber using a robotic acoustic-field scan behind the barrier. The results confirm an increased IL and a dual-regime behaviour achieved through a 90° rotation of the scatterers.