This spoiler free chapter of the guide to The Last of Us 2 has a walkthrough for Abby's sequence during which she heads to Jackson to find a certain person.
Escape from the infected
You start this sequence by facing a few runners. You can defeat them with weapons - there isn't much room for sneaking around. However, you will soon find that the fight is futile and begin the escape sequence.
Run forward and stay close to the right side. Go over the truck and keep running down. Jump over the bridge and run down, pass a destroyed building, and jump out a window.
Jump on the protruding containers and jump to the other side of the gate. If you are injured, you will find an alley nearby - you have enough time to heal. Move along the gate with the runners - Joel will save you at the last minute.
Fight in the hangar
Follow Joel and walk through the door. You have a moment to, for example, get a melee weapon by ripping a pipe out of a wall. Heal yourself, gather supplies and then continue the way forward.
Time for a fight with runners who start attacking the lift station. There will be a few waves of them, so be careful. You also have to help Joel push the gondola. Defend Tommy against attacks and help Joel kill the enemies. Watch out for the clicker - if you don't have a special melee weapon, it will kill you instantly when it gets closer.
Use the gondola to jump out of the hangar and run after Joel and Tommy. Watch the cut-scene.
As Ellie, go towards the building. Go inside and search the area, then walk down to see and incredibly traumatic scene for Ellie...
You now move to Jackson. Follow Dina home - upstairs, approach the bed and open the box. Go downstairs and talk to Dina and Maria. This will end the sequence in Jackson.