Shortcode for pulling specific Post Title outside loop when ID is passed in

Codex documentation for shortcodes has a section on Handling Attributes.

In a nutshell attributes will get passed on to your callback and you need to implement handling them with your code within it:

function my_shortcode_handler( $atts, $content = null ) {
    $a = shortcode_atts( array(
        'attr_1' => 'attribute 1 default',
        'attr_2' => 'attribute 2 default',
        // ...etc
    ), $atts );
}