Show/Hide Column in Views Table
I am not sure if this is The Drupal Way to fix this, but I fixed it with jQuery hide() and show(). 

// Hide the Name Column when Nick Name is shown
$('#edit-dyfield-field-girls-nickname').change(function() {
                if ($('#edit-dyfield-field-girls-nickname').is(':checked')) {
                    $(document).ajaxStop(function() { // Forcefully stopping Ajax function in the page as other ajax load was main culprit in my case
                        $('.views-field-title').hide();
                    });
                }

                if ($('#edit-dyfield-field-girls-nickname').is(':not(:checked)')) {
                    $(document).ajaxStop(function() {
                        $('.views-field-title').show();
                    });
                }

            });


Note: In the above example jQuery toggle() doesn't work, so, I have to put 2 if(){} statements for Check and UnCheck.