We propose an enhanced deep learning-based model for image segmentation of the left and right ventricles and myocardium scar tissue from cardiac magnetic resonance (CMR) images. The proposed technique integrates UNet, channel and spatial attention, edge-detection based skip-connection and deep supervised learning to improve the accuracy of the CMR image-segmentation. Images are processed using multiple channels to generate multiple feature-maps. We built a dual attention-based model to integrate channel and spatial attention. The use of extracted edges in skip connection improves the reconstructed images from feature-maps. The use of deep supervision reduces vanishing gradient problems inherent in classification based on deep neural networks. The algorithms for dual attention-based model, corresponding implementation and performance results are described. The performance results show that this approach has attained high accuracy: 98% Dice Similarity Score (DSC) and significantly lower Hausdorff Distance (HD). The performance results outperform other leading techniques both in DSC and HD.