In recent years, target detection has drawn increasing attention in the field of radar signal processing. We consider the problem of coherent integration for detecting a highly maneuvering target with complex motion, involving range migration (RM), linear Doppler frequency migration, and quadratic Doppler frequency migration within the coherent interval. Owing to the different sensitivity of the envelope and phase to the target motion, the parametric and nonparametric models are, respectively, established. A coarse-to-fine integration algorithm is correspondingly proposed. Specifically, the keystone transform and fold factor searching are first utilized to remove the parametric RM and to achieve coarse integration. Then, the embedded phase gradient autofocus is applied to estimate the nonparametric nonlinear Doppler phase and realize refined integration. Compared with several representative algorithms, the proposed method could achieve a good trade-off between computational complexity and detection performance. Moreover, this method can be easily extended to detect a high-order maneuvering target. Finally, both simulations and real data experiments are presented to demonstrate the effectiveness of the proposed method.