Video microscopy, when combined with machine learning, offers a promising approach for studying the early development of in vitro produced (IVP) embryos. However, manually annotating developmental events, and more specifically cell divisions, is time-consuming for a biologist and cannot scale up for practical applications. We aim to automatically classify the cell stages of embryos from 2D time-lapse microscopy videos with a deep learning approach. We focus on the analysis of bovine embryonic development using video microscopy, as we are primarily interested in the application of cattle breeding, and we have created a Bovine Embryos Cell Stages (ECS) dataset. The challenges are three-fold: (1) low-quality images and bovine dark cells that make the identification of cell stages difficult, (2) class ambiguity at the boundaries of developmental stages, and (3) imbalanced data distribution. To address these challenges, we introduce CLEmbryo, a novel method that leverages supervised contrastive learning combined with focal loss for training, and the lightweight 3D neural network CSN-50 as an encoder. We also show that our method generalizes well. CLEmbryo outperforms state-of-the-art methods on both our Bovine ECS dataset and the publicly available NYU Mouse Embryos dataset.