For Shipment Tracking version 1.4.0 or above

shipment-tracking.php

<?php

$order_id = method_exists($order, 'get_id') ? $order->get_id() : $order->id;

//getting shipping details
$objWC_Shipment = WC_Shipment_Tracking_Actions::get_instance();
$shipping_details = $objWC_Shipment->get_tracking_items($order_id);
if (!empty($shipping_details)) {
    foreach ($shipping_details as $shipping_detail) {
        $order_data['shipping_details'][] = array(
            'tracking_provider' => $shipping_detail['tracking_provider'],
            'tracking_number' => $shipping_detail['tracking_number'],
            'date_shipped' => $shipping_detail['date_shipped']
        );
    }
}