Legged locomotion is not just about mobility; it also encompasses crucial objectives such as energy efficiency, safety, and user experience, which are vital for real-world applications. However, key factors such as battery power consumption and stepping noise are often inaccurately modeled or missing in common simulators, leaving these aspects poorly optimized or unaddressed by current sim-to-real methods. Hand-designed proxies, such as mechanical power and foot contact forces, have been used to address these challenges but are often problem-specific and inaccurate. In this paper, we propose a data-driven framework for fine-tuning locomotion policies, targeting these hard-to-simulate objectives. Our framework leverages real-world data to model these objectives and incorporates the learned model into simulation for policy improvement. We demonstrate the effectiveness of our framework on power saving for quadruped locomotion, achieving a significant 24-28\% net reduction in total power consumption from the battery pack at various speeds. In essence, our approach offers a versatile solution for optimizing hard-to-simulate objectives in quadruped locomotion, providing an easy-to-adapt paradigm for continual improving with real-world knowledge. Project page https://hard-to-sim.github.io/.