Plastic Left Ice Bucket Shelf (slide) at the back broke around the pop rivet into the shelf .

At the front of the shelf there is a Phillips metal sheet metal screw that holds the front of the shelf in place. Its removal was fairly set straight forward but removing the pop rivet was awkward and took some time to drill out from the rear metal shelf. Once the rivet was out, it was easy finding a small screw that would hold the shelf in place since I didn't have any pop rivets that would fit sufficiently tight or long enough.