How do I completely get rid of a potentially compromising picture?
I received a potentially compromising picture in a WhatsApp chat


So someone else sent it to you. 

If you delete the image from within the application, emptied the trash, checked your photo stream / iPhoto folders, deleted the contents of Library/Caches on any computers linked to the same service account, and checked Time Machine in the same locations it is highly unlikely that it still exists on your computer.

But someone else still has the original.

As many public figures have discovered, it's more-or-less impossible to permanently delete an image once someone else has it.