This spoiler free chapter of the guide to The Last of Us 2 has a walkthrough of the Road to the Aquarium stage taking place during the events of Seattle Day 3.
Road to The Aquarium
Go see Jesse and Dina at the theater. After the cut-scenes, follow Jesse. You can also search the nearby buildings. Enter the red building (break the glass) and, together with Jesse, move the bookshelf to reveal a passage.
You will come across a team of WLF soldiers. It is good to distract enemies, for example, by throwing a brick at the window nearby to provoke them to split up. Then you can start killing them quietly. There aren't many of them - you and Jesse should be able to handle the threat.
Enter the building, go upstairs, and follow the edge to the other side of the building. Then move on and climb the blue truck to the next area.
Climb up the abandoned vehicles, and you will see a Ferris wheel in the distance. Swim under the obstacles, climb onto the truck, and move on.
Then, with Jesse's help, climb up to the reading room. Go upstairs and jump down through a hole in the floor. Move forward, and you will see a WLF prisoner die at their hands.
Fight the enemies. You can eliminate them either through stealth or by using firearms. First, however, locate a patrol with a dog - they can thwart your plans.
Now enter the building, go upstairs, climb the scaffolding, and head towards the river.
Swim under the bus, go left and then keep climbing ruins until you reach the top.
At the top, follow Jesse - squeeze through the narrow passages and remove obstacles in your path. Dive under the obstacle, follow the man, then climb up the line.
Getting a boat
This is one of the more extensive combat sequences in the game. Your goal is to reach the boat, but it is guarded by a very large group of enemies located on different floors of the building. You have to be methodical in killing enemies - do that slowly, floor by floor. Of course, if you feel up to it, you can always make a direct attack.
When there are few enemies left, you can take a chance by falling into the water, quickly starting the boat (it takes a few moments, unfortunately) and sailing away.