Motion retargeting is a promising approach for generating natural and compelling animations for nonhuman characters. However, it is challenging to translate human movements into semantically equivalent motions for target characters with different morphologies due to the ambiguous nature of the problem. This work presents a novel learning-based motion retargeting framework, Adversarial Correspondence Embedding (ACE), to retarget human motions onto target characters with different body dimensions and structures. Our framework is designed to produce natural and feasible character motions by leveraging generative-adversarial networks (GANs) while preserving high-level motion semantics by introducing an additional feature loss. In addition, we pretrain a character motion prior that can be controlled in a latent embedding space and seek to establish a compact correspondence. We demonstrate that the proposed framework can produce retargeted motions for three different characters -- a quadrupedal robot with a manipulator, a crab character, and a wheeled manipulator. We further validate the design choices of our framework by conducting baseline comparisons and a user study. We also showcase sim-to-real transfer of the retargeted motions by transferring them to a real Spot robot.