Some thoughts. You can complete it in one sitting.
(1) You will need to earn about 15M credits to buy enough frigates so that you can complete the mission where you complete three frigate missions. I recommend putting some expensive sellable items into the expedition so you can get this started as soon as you finish the first milestone. This is the only timed element to the expedition.
(2) Completing the mission to visit 8 uncharted systems is harder than it sounds. Everyone is fanning out, so you'll have to jump a long way from the path to find uncharted systems. I recommend just stocking up on warp fuel and doing this last.
(3) The most annoying time consuming mission is fishing for 5 uncommon icy fish. Find someone's existing fishing outpost to speed this up once you have the fishing rod.
(4) At one point in the fifth phase, you're supposed to wait for community research. Except you can buy the item for quicksilver right away without waiting. The tooltips are a bit wrong here. Just go to the quicksilver synthesis companion on the space anomaly.
(5) Getting the Normandy is cool if you missed expedition 2 previously. Nice that the reward is a frigate and not just another ship for the collection. It has a special class, "Recon".
Overall, can be done in one sitting if you start the frigate missions as early as possible. Don't worry about the community research.