Main Quest - A Dubious Drive
Not much to do here besides follow Ardyn's car again. Noctis will be at the wheel this time though so in case you have left the driving to Ignis all this time, it's worth noting that you can't really go wherever you want, whenever you want when at the wheel. Instead it's more like driving on rails and pretty much impossible to go off course. You still have to make the major turns yourself though.
In any case, drive to the Coernix Station and camp there if you want. Otherwise, feel free to look around for freebies and also check for sidequests. But first, take a listen to the people standing around the radio to get a scene and some funny banter. Ardyn will be waiting in the shop here and only talk to him if you're certain to have done everything you want to, as you won't have access to the Regalia for a while after this.
Main Quest - Onward to the Disc
You will be following Ardyn's car again until it reaches the imperial blockade. After he gets the gate to open up, drive a little further along the rocky path on your own.
It will soon narrow down and you will have to continue on foot to the royal tomb at the end. Grab the Blade of the Mystic here to trigger a scene.
Main Quest - The Archean
You will end up in a small dungeon at the bottom of the cliff with only Gladio for company. The path here is very straightforward so get a move on while keeping an eye out for molten rocks on the path. Try not to stand on these spots too long if you can't entirely avoid them, as it overheats your characters and gradually depletes their HP. There are plenty of fire and lightning mineral deposits for you to harvest as well so stock up on these. Moving on, head for the destination marker and follow Gladio across the narrow ledge. Grab the Mega Phoenix on the other side, harvest the mineral deposits before ducking through the hole.
It will soon come to a point where Gladio decides he's tired of hearing Noctis complain and demands an answer. Saying "yes" increases Noctis's strength by 50% -- a welcome boost for the battle against Titan later. There is a Mega-Potion some ways further down the path and you'll receive a call from Ignis warning you of imperial presence. Defeat the small contingent of level 18 magitek soldiers to complete this bit of the story quest.
Main Quest - The Trial of Titan
Move forward a little bit here and the objective should change telling you to fend for your life. There's not much you can do for the time being apart from hold the block button in an attempt defend against Titan's foot. Then you can officially start start running after being saved by Gladio. Roll to avoid Titan's punches and keep moving until the next objective change.
This time you will have to block and parry Titan's attacks. Do this twice and you'll be able to counter after the second time. The battle to destroy Titan's arm will begin after this. Look up so you can see the incoming hand to effectively block and parry, which will in turn make Titan put his arm down putting it within reach of your attacks. Ice spells work quite well so use them when you can. Titan can also do sweeping strike which you can avoid more effectively by using the warp points in the area.
Prompto and Ignis soon joins the fray so keep hacking the arm and use Armiger Chains when they're available to you. And once you've dealt enough damage, a strategy requiring you to deal 15000 total damage will appear. Use techniques, link strikes and everything else to achieve this so Prompto and Ignis can use Blizzara on Titan. And when they do, be sure to hit the attack button at the end for Noctis to perform a finisher that ends the battle.