UPDATE sales_order SET state='complete', status='complete' WHERE status = 'processing'
UPDATE sales_order_grid SET status='complete' WHERE status = 'processing'

INSERT INTO `sales_order_status_history` (`parent_id`, `is_customer_notified`, `is_visible_on_front`, `comment`, `status`, `created_at`, `entity_name`) VALUES (1, 0, 0, NULL, 'complete', NOW(), 'order');

mysql> UPDATE sales_order SET state='complete', status='complete' WHERE increment_id IN (000043719,000044003,000044117,...);
Query OK, 15 rows affected (0.08 sec)
Rows matched: 16  Changed: 15  Warnings: 0

mysql> UPDATE sales_order_grid SET status='complete' WHERE increment_id IN (000043719,000044003,000044117,...);
Query OK, 15 rows affected (0.03 sec)
Rows matched: 16  Changed: 15  Warnings: 0