If you want to change the heading levels for widgets in a sidebar, you shouldn’t use actions or filters or css to override WordPress: what you do is change how the sidebar is *defined* when it is first initialised.

If your theme uses a sidebar, it has to register it first. Somewhere in your theme (usually in your functions.php file) you will find a call to the register_sidebar( $args ); function, where $args is either a string or an array that defines how the sidebar is structured.

If there are no arguments for the register_sidebar() call then the defaults are used – this is to use h2 for the widget titles. If you want to use a different heading (or none at all) then you need to set the values for 'before_title' and 'after_title' when you call register_sidebar() like this:

 __( 'Right Hand Sidebar' ),
  'id' => 'right-sidebar',
  'description' => __( 'Widgets in this area will be shown on the right-hand side.' ),
  'before_title' => '
',
  'after_title' => '
'
));
?>