Underwater Image Enhancement (UIE) is a crucial preprocessing step for underwater vision tasks. Addressing the challenge of training supervised deep learning models on large, diverse datasets while learning the intrinsic degradation factors of underwater images is essential for improving model generalization performance. In this paper, we propose a Weak-Strong Dual Supervised Generative Adversarial Network (WSDS-GAN) for UIE. During the first weakly supervised learning phase, unpaired images, consisting of degraded underwater images and clear in-air images, are used to train the model with the goal of recovering color, brightness, and content. In the second strongly supervised learning phase, a limited number of paired images are fed into the model to further train the image detail recovery generator. Comprehensive experiments on public datasets and self-photographed images demonstrate the effectiveness of our proposed method over existing state-of-the-art methods, both qualitatively and quantitatively. Additionally, we show that our method significantly enhances image details to support subsequent underwater vision tasks.