Display a form partially with a shortcode

In your function mailchimp_form_shortcode(), you need to do following changes (specifically first line inside the function):

<?php
function mailchimp_form_shortcode($atts) {
    extract(shortcode_atts(array(), $atts));

    if(isset($attrs['type']) && $attrs['type'] == 'some_value'){
            //return "form element";
    }

}
add_shortcode('mailchimp', 'mailchimp_form_shortcode');
?>

and your shortcode will be as:

[mailchimp type="some_value"]

By this, you can pass parameters to your shortcode function.
And inside that shortcode function, you can display the form elements based on the passed parameters.

Hope this will help you.