Plant seedling segmentation supports automated phenotyping in precision agriculture. Standard segmentation models face difficulties due to intricate background images and fine structures in leaves. We introduce UGDA-Net (Uncertainty-Guided Dual Attention Network with Entropy-Weighted Loss and Deep Supervision). Three novel components make up UGDA-Net. The first component is Uncertainty-Guided Dual Attention (UGDA). UGDA uses channel variance to modulate feature maps. The second component is an entropy-weighted hybrid loss function. This loss function focuses on high-uncertainty boundary pixels. The third component employs deep supervision for intermediate encoder layers. We performed a comprehensive systematic ablation study. This study focuses on two widely-used architectures, U-Net and LinkNet. It analyzes five incremental configurations: Baseline, Loss-only, Attention-only, Deep Supervision, and UGDA-Net. We trained UGDA-net using a high-resolution plant seedling image dataset containing 432 images. We demonstrate improved segmentation performance and accuracy. With an increase in Dice coefficient of 9.3% above baseline. LinkNet's variance is 13.2% above baseline. Overlays that are qualitative in nature show the reduced false positives at the leaf boundary. Uncertainty heatmaps are consistent with the complex morphology. UGDA-Net aids in the segmentation of delicate structures in plants and provides a high-def solution. The results showed that uncertainty-guided attention and uncertainty-weighted loss are two complementing systems.