Play through the story until you get the Construction Worker, this is pretty early on in the story, by the way.
Then play as the Construction Worker so you can call in the Cargo Drone by holding down
. Once you have the drone, fly it as close to the Parcel Fox delivery point as it will fit, so it's very close by you. Interact with the Parcel Fox delivery point and be sure to find a delivery that does not have a timer. The icon on the top left of each delivery is the timer and you want the blue line next to it to be empty.
Keep in mind that each time you drop out of the Delivery Fox menu and re-enter, the deliveries will change. So keep dropping in and out of the menu until you get a delivery with no timer.
Once you start the delivery, quickly hop on your Cargo Drone by pressing
next to it. Once on top, aim the camera down and tap
to hijack it, and hold
to make it fly up and use the left stick to pilot it away. Obviously, avoid crashing into anything and be sure there's nothing above you, but start moving toward the Yellow marker the game will give for the delivery point, be sure to fly as high as possible (hold
until the drone will no longer gain altitude).
If the delivery you chose is Contraband (the icon on the top right when you selected the job), you'll have drones spawn occasionally, but as long as you keep moving, they'll not spot you and fall behind. Eventually they lose track and the alert will cease, leaving you to leisurely float to the delivery point - very ideal for Fragile Deliveries (middle icon on top of delivery select window). Keep in mind I'm playing on Easy, so that might have some affect on how aggressive the drones might be.
It's a little slow and bit less adventurous than driving everywhere under a time constraint, but it'll get everything done without a whole lot of fuss.