In classic GIFTS, we were able to open all pending applications in our workspace and bulk tax status verify and check watchlist. In Skyview, it doesn't have that option and having to find the matching nonprofit will be very time consuming.
We will take a look at adding this to the list of batch actions for requests in SKY view. In the meantime, you can perform this action for a list of organization records (or in the case of the "Check watchlists" action, contact records as well).
If you tend to start from a list of request records, the easiest way to do this today is to select the checkboxes for all of the request records, then click "Find related", then "Organizations". Now you've got a list of organizations related to each request, and you can click "Select all" > "Due diligence" > "Tax status verify".