Elias here with Shopify Support. That's a great question!
You can bulk print packing slips by using our free app, Order Printer, which comes with a packing slip template. We also have a guide for using the Order Printer app and you can modify the templates to your preference. If you need any help with customizing the template, this is something that our Theme Support can assist you with as well.
Once your packing slip template is good to go, you can use bulk actions to print up to 50 packing slips from your admin or mark your orders as fulfilled.
If you're using Shopify Shipping for your shipping labels, you can also bulk purchase and print shipping labels for up to 20 orders.
Let me know if this is what you're looking for?