Main Quest - No Turning Back
Head for the front of the train while fighting off Shaga and Gargoyle monsters. Keep at until the next objective pops up. Now just hold out and continue clearing enemies until the train exits the tunnel, before finally rolling to a stop in Tenebrae.
Main Quest - Where She Lived
Start by going in the opposite direction instead of following Aranea, to find a Reflex Enhancer behind some crates at the end of the platform. Then go all the way to the other side for a Muscle Stimulant. Follow Aranea so she can introduce you to Biggs and Wedge. Speak to Biggs next and he'll tell you about Maria wanting to discuss a few things. There are shops near Aranea's ship as well, although they don't really offer anything new equipment-wise. So just stock up on consumables before moving on. And be sure to listen to the discussion between your companions and Aranea. Also look by the rock next to the mech for a Magitek Booster.
Cross the bridge and pick up the Sky Gemstone on the ground. Speak with Maria to proceed then head for the train. Be sure to talk with Aranea again on the way back as she has more to say. Moving on, grab the Flesh Fortifier up ahead after your encounter with the little girl. Go ahead and board the train to Gralea afterwards.
Main Quest - Into the Arctic Crevasse
Once you're free to explore the train, go to the rear and check all the cars for plenty of freebies including an Elixir, a Chrome Bit, a Mega Phoenix, a Debased Banknote, a Hi-Elixir, a Rusted Bit, an Electrolytic Condenser, and a Gralean Medal of Distinction.
Make your way back to the front of the train when you have everything, and this part of the story ends after Noctis receives a call from somebody.
Main Quest - Breath of the Glacian
Here you start with having to defeat a group of monsters outside the train. There will Shagas and Wraiths in the intial wave, after which a level 34 Deathclaw shows up after the first group is dealt with. Kill the thing so you can reboard the train and meet up with Ardyn yet again.
Go after him to initiate a series of story events which end with Noctis receiving his next royal arm, the Trident of the Oracle, alongside Shiva's blessing. Now turn around and attack the frozen Ardyn to trigger the closing sequences for this chapter.