The healthy operation of aircraft engines is crucial for flight safety, and accurate Remaining Useful Life prediction is one of the core technologies involved in aircraft engine prognosis and health management. In recent years, deep learning-based predictive methods within data-driven approaches have shown promising performance. However, for engines experiencing a single fault, such as a High-Pressure Compressor fault, existing deep learning-based predictive methods often face accuracy challenges due to the coupling relationship between different fault modes in the training dataset that includes a mixture of multiple fault modes. In this paper, we propose the FC-AMSLSTM method, a novel approach for Remaining Useful Life prediction specifically targeting High-Pressure Compressor degradation faults. The proposed method effectively addresses the limitations of previous approaches by fault classification and decoupling fault modes from multiple operating conditions using a decline index. Then, attention mechanisms and multi-scale convolutional neural networks are employed to extract spatiotemporal features. The long short-term memory network is then utilized to model RUL estimation. The experiments are conducted using the Commercial Modular Aero-Propulsion System Simulation dataset provided by NASA. The results demonstrate that compared to other prediction models, the FC-AMSLSTM method effectively reduces RUL prediction error for HPC degradation faults under multiple operating conditions.