in theory it should work like that (untested!):

/**
 * Validate the extra register fields.
 *
 * @param  string $username          Current username.
 * @param  string $email             Current email.
 * @param  object $validation_errors WP_Error object.
 *
 * @return void
 */

function wooc_validate_extra_register_fields( $username, $email, $validation_errors ) {

    if ( isset( $_POST['first_name'] ) && empty( $_POST['first_name'] ) ) {
        $validation_errors->add( 'first_name_error', __( '<strong>Error</strong>: First Name is required!.', 'woocommerce' ) );
    }

    if ( isset( $_POST['last_name'] ) && empty( $_POST['last_name'] )  ) {
        $validation_errors->add( 'last_name_error', __( '<strong>Error</strong>: Last Name is required!.', 'woocommerce' ) );
    }
}

add_action( 'woocommerce_register_post', 'wooc_validate_extra_register_fields', 10, 3 );

http://stackoverflow.com/questions/24245283/woocommerce-registration-form-validation-not-working

usually if there is an error in the form something like this is displayed:

<ul class="woocommerce-error">
    <li><strong>Fehler:</strong> <strong>Error</strong>: Anrede is required!</li>
</ul>
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