High-performance computing (HPC) is reshaping computational drug discovery by enabling large-scale, time-efficient molecular simulations. In this work, we explore HPC-driven pipelines for Alzheimer's disease drug discovery, focusing on virtual screening, molecular docking, and molecular dynamics simulations. We implemented a parallelised workflow using GROMACS with hybrid MPI-OpenMP strategies, benchmarking scaling performance across energy minimisation, equilibration, and production stages. Additionally, we developed a docking prototype that demonstrates significant runtime gains when moving from sequential execution to process-based parallelism using Python's multiprocessing library. Case studies on prolinamide derivatives and baicalein highlight the biological relevance of these workflows in targeting amyloid-beta and tau proteins. While limitations remain in data management, computational costs, and scaling efficiency, our results underline the potential of HPC to accelerate neurodegenerative drug discovery.