Go to Design Studio.
Click Landing Pages.
Hold Ctrl (Windows) or Command (Mac) and click to select multiple landing pages.
Do not click the actual landing page name, those are links and will take you to the page itself.
With your landing pages selected, go to Landing Page Actions and click on Approve.
There you go! You can now quickly and easily approve multiple landing pages.
You can also use the steps above for other bulk options, such as unapprove or delete.