I don't believe a single API call will get you this result, I think you'll have to make the "/boards" call on the category to get the list of boards, then make the "/board/board_id/metrics" on each board to get the "board_views" for that board. You can sort the list as you create it. The disadvantage is that this might be time/resource intensive, and might slow down the page load time.
One way to get around that might be to write this code in an endpoint, and implement caching, so you only have to make this call once every couple of seconds/minutes/hours. You can then make the call to the endpoint from any component to get the sorted list.