The increasing energy needs of supercomputers have highlighted the importance of energy efficiency for HPC and AI tasks. Accelerated Processing Units (APUs), which combine CPU and GPU in a package with shared memory, have the potential to enhance energy efficiency by reducing data movement. Nevertheless they bring management challenges. As opposed to conventional setups where CPUs, GPUs and memory have separate power allocations, APUs rely on a power limit that necessitates flexible distribution. Inefficient power allocation can lead to improper resource utilization and can hinder performance improvements while also raising concerns about energy usage. This research investigates methods for improving energy efficiency in APU systems with the High Performance Linpack Benchmark (HPL). We analyze the findings of the Adastra-2 partition of CINES, which ranked third on the SC24 Green500 list. This includes fixed resource utilization approaches, architectural challenges, and memory side effects. In addition, we offer recommendations on how to improve the efficiency of HPL runs, discuss power management strategies, and pinpoint areas where performance can be further enhanced. Our discoveries provide practical system guidelines for future APU-based HPC deployments.