You can fulfill an order is by fulfilling the N fulfillment-orders that compound the order.
The workflow would be to get all the fulfillments orders asociated to an order: Doc Here
You get an array with the N fulfimments orders that compount the order.
Then you should get the id of each of those fulfillment orders and fulfill each of them: Doc Here
Once you had fulfilled all the fulfillments orders of the order, the order would be fulfilled.
I hope that it help you.
EDIT: Make sure you have this access scope so you can have access to the fulfill fulfillments orders api.
- write_merchant_managed_fulfillment_orders