Change the filter category order in Expression
WordPress by default doesn’t provide an order option to the categories. One way to set a custom order to your filter categories of the gallery page would be to order them by their slug. To do this you have to modify line 19 of the includes/gallery-load.php file:
$args=array("hide_empty"=>false, "hierarchical"=>true);
to be like this:
$args=array("hide_empty"=>false, "hierarchical"=>true, 'orderby'=>'slug');
with this modification your categories will be ordered by slug, so by editing their slug you can change the order. One option would be to append a number like this:
1-photography
2-landscapes
3-portraits