Transcranial focused ultrasound (tFUS) has emerged as a promising non-invasive modality for precision neuromodulation. However, the heterogeneous acoustic properties of the skull often induce phase aberrations that shift the ultrasound focus and compromise energy delivery. In this study, we developed and validated a phase-reversal based aberration correction method to enhance the targeting specificity of tFUS using a 128-element random array ultrasound transducer. Individual head models were constructed from T1-weighted magnetic resonance (MR) images and corresponding pseudo-computed tomography (pCT) data to accurately represent subject-specific skull geometries and the targeted left V5 (V5L) region. Acoustic simulations were conducted with the k-Wave toolbox by first acquiring free-field pressure waveforms and then recording the aberrated waveforms in the presence of the skull. The phase differences between these conditions were used to compute corrective delays for each transducer element. Quantitative evaluation using metrics such as focal overlap with the target region, axial focal positioning, and the delivered ultrasound energy demonstrated significant improvements: the overlap volume increased by 98.70%, mean axial positioning errors were reduced by up to 14.36%, and energy delivery to the target improved by 17.58%. We further demonstrated that the proposed approach outperforms the conventional ray-tracing methods. The results show that phase-reversal based aberration correction markedly increases the spatial targeting accuracy of tFUS and enhances the efficiency of focused ultrasound energy deposition for the customized random array transducer, paving a way for effective and personalized non-invasive neuromodulation therapies.