Hey @Andrew_Hewitt1
At the moment you do need to click into each task to mark it complete within a boards project. That said, I invite you to up-vote the following post in our feedback category, for multi-select, which would speed up the process of completing more than one task at a time.
One workaround I can offer would be to run an advanced search of tasks in this project (if you have a premium plan) then multi-select the tasks you wish to mark complete, & do so in the Task pane to the right. The changes you make here, will then be reflected in your boards project as well!
Hope this helps!