To unlock the Online Order department, you will need to unlock Storage 00, 01, 04, 08, and 09. Then you have the ability to purchase the Order Packing department for $80,000. You will also need to purchase the Parcel Pickup Point in the Devices tab. You will have to manually turn on the Online Orders and eventually one will come in. You will need to purchase 'Organizer: Trays' to manually do orders, or hire someone to work in the Packaging Department and they will do it for you. You will accept the order in one of the locations and then pick the items from either your backroom or on the sales floor. Once the order has been packed and put into the Parcel Pickup a customer will come and pick it up and you will get paid. You can check the progress towards the achievement on the Manager Blackboard under the Statistics section. Once "Online Orders Assembled" reaches 25 you are good.
This achievement will unlock after you close the store for the night after you package you have completed 25 online orders.