Cells are essential to life because they provide the functional, genetic, and communication mechanisms essential for the proper functioning of living organisms. Cell segmentation is pivotal for any biological hypothesis validation/analysis i.e., to get valuable insights into cell behavior, function, diagnosis, and treatment. Deep learning-based segmentation methods have high segmentation precision, however, need fully annotated segmentation masks for each cell annotated manually by the experts, which is very laborious and costly. Many approaches have been developed in the past to reduce the effort required to annotate the data manually and even though these approaches produce good results, there is still a noticeable difference in performance when compared to fully supervised methods. To fill that gap, a weakly supervised approach, PACE, is presented, which uses only the point annotations and the bounding box for each cell to perform cell instance segmentation. The proposed approach not only achieves 99.8% of the fully supervised performance, but it also surpasses the previous state-of-the-art by a margin of more than 4%.