Save & Keep Working/Required Fields

You need to give them the ability to save even if the form is barely completed. But then at the top of the form you will construct a long warning message telling them which fields they need to complete. Feel free to post back if you need help with the syntax for that. Then you need to give them the option to either push a button or check a checkbox or set a multiple-choice field to set the status of the record to "Submitted".   You will prevent them from being able to edit that field if there are warnings about missing fields.  

Then you tell who is ever at the other end of these records that are being created to know only to act on records which have been "Submitted" and not those which are still "In Process".