This paper aims to address electromagnetic scattering problems in multiple bodies of revolution (MBoR) through a hybrid heterogeneous acceleration framework derived from equivalence principle algorithm (EPA). The computational workflow under EPA scheme is systematically divided into three dominant processes: matrix filling, LU-based direct solver, and iterative solver. To enhance matrix filling efficiency, a co-processing framework is proposed where the CPU is responsible for partitioning matrices in a block-wise manner by Message Passing Interface (MPI) while intensive computation operations are assigned to heterogeneous accelerators. A loop reduction is also proposed for matrix filling, achieving a peak speedup of 162-fold in matrix filling relative to CPU-only implementations. To solve current on internal BOR, a parallel LU-based direct solver is developed, where matrix operators are delegated to heterogeneous accelerators, including a dual-matrix operator designed for simultaneous inversion of upper/lower matrices, achieving a peak speedup of 150-fold under large-scale datasets. To acquire current solution across the entire solution domain, the generalized minimal residual method (GMRES) is parallelized by a multi-tier reduction framework, where inter-subdomain interaction computations are calculated simultaneously by MPI. A heterogeneous-accelerated matrix-vector multiplication (MVM) operator is designed based on the Fourier-mode characteristics of BoR basis functions, which can achieve a peak speedup of 10-fold under large-scale datasets. Finally, parallelization of parameter sweeping is validated through several simulation and experimental benchmarks.