Low-cost accelerometers play a crucial role in modern society due to their advantages of small size, ease of integration, wearability, and mass production, making them widely applicable in automotive systems, aerospace, and wearable technology. However, this widely used sensor suffers from severe accuracy and range limitations. To this end, we propose a honed-energy regularized and optimal supervised GAN (HEROS-GAN), which transforms low-cost sensor signals into high-cost equivalents, thereby overcoming the precision and range limitations of low-cost accelerometers. Due to the lack of frame-level paired low-cost and high-cost signals for training, we propose an Optimal Transport Supervision (OTS), which leverages optimal transport theory to explore potential consistency between unpaired data, thereby maximizing supervisory information. Moreover, we propose a Modulated Laplace Energy (MLE), which injects appropriate energy into the generator to encourage it to break range limitations, enhance local changes, and enrich signal details. Given the absence of a dedicated dataset, we specifically establish a Low-cost Accelerometer Signal Enhancement Dataset (LASED) containing tens of thousands of samples, which is the first dataset serving to improve the accuracy and range of accelerometers and is released in Github. Experimental results demonstrate that a GAN combined with either OTS or MLE alone can surpass the previous signal enhancement SOTA methods by an order of magnitude. Integrating both OTS and MLE, the HEROS-GAN achieves remarkable results, which doubles the accelerometer range while reducing signal noise by two orders of magnitude, establishing a benchmark in the accelerometer signal processing.