Click on Posts > Categories and mouse-over each category link. In your browser’s status bar, you will see a URL similar to this:
http://www.yoursite.com/wp-admin/edit-tags.php?action=edit&taxonomy=category&tag_ID=135&post_type=post
Note the tag_ID number for each category you don’t want to show on the menu.
Go to Appearance > Editor, click archive.php (Theme Archive). At the top is this array of options:
<?php $tabcats = array(
'show_option_all' => '',
'orderby' => 'name',
'order' => 'ASC',
'style' => 'list',
'show_count' => 0,
'hide_empty' => 1,
'use_desc_for_title' => 1,
'child_of' => 0,
'feed' => '',
'feed_type' => '',
'feed_image' => '',
'exclude' => '|',
'exclude_tree' =>' ',
'include' =>' ',
'hierarchical' => true,
'title_li' => __( ' ),
'show_option_none' => __('),
'number' => null,
'echo' => 1,
'depth' => 1
); ?>
Place your cursor between the two single-quotes in the ‘exclude’ option and enter the tag_ID numbers, separated by commas. For example:
'exclude' => '156, 44',
Click Update File. You should now only see the categories you want in the menu on all archive pages for Standard Posts.