If you didn't already figure this out, to print multiple shipping labels for a single order do the following:
open the order
choose Create Shipping Label
mark all items to zero that are not in the box you want the label for
choose package dimension, weight and service provider
Choose purchase label
print the label
return to the order and do the same until all items are fulfilled and you have created a label for each package
May I know which carriers you use to handle shipping? Or do you use any app?
In case you are using FedEx, the Shopify FedEx app would be the perfect solution for you. With the app, you can automate the packing process based on the product weight, product dimensions or you can even pack each of your items individually. You can set the process according to your requirement and you can also create custom boxes of your choice. Labels can be generated based on the number of boxes to be shipped.