Shenmue

This is part of the story and therefore unmissable. The steps for this part of the story are:

After you have found the mirror and got the trophy Stab in the Dark, you should now take the mirror to Master Chen.

A side note, this is a good time to get another trophy out of the way first. This is you just have to go to both antique stores (1 & 2) in town to get this one (save beforehand as it may not unlock first try).

Continuing with this trophy, you need to phone before heading to the warehouse so you can get past the guard. You can phone from your house, or any other phone. I used one at the entrance to the docks near the bus stop.

Phone number 0468-61-564. When you phone, you will need to response to the password again:
"Father's Heaven
Nine Dragons
Mother's Earth
Comrades"

Now head to the old warehouse 8 and speak with Master Chen. You will have a small QTE to deal with here. At the end of this scene, you will be back home. Have a cutscene and get some sleep.

When you wake, you will get some money. Then go to Fuku-san's room across and to the right of yours. Now you need to head into town to the either of the travel agencies. On your way, I would recommend going passed the shrine to get After that, head to any of the travel agencies (3&4) and find out you don't have enough money. Next talk to Fuku-san at home again and he will give you his money. It still isn't enough, but he tells you to go see Nozomi outside the flower shop (5). She will tell you to try going by boat. Head to the Asia Travel Co (3) and give them your money. They will tell you to come back in 4 hours. So wait for 4 hours and head back inside. If there is no one inside, you are too early so leave and come back later.

The woman you gave the money to is gone and replaced by 3 guys, a cutscene will have you beat them up and you are told to meet him at You arcade (6) the next day at 12PM. So go sleep and then head to You Arcade for 12PM. In here, you will get in a tough fight. You don't have to win (I didn't). I have read there is no reward for winning either. If you fail, you will be taken home to sleep and wake up the next day.

Now head to the Asia Travel Co (3) again and the guy will run. You have a long QTE sequence here. Going left and right a lot, with X to jump. At one point you take 2 lefts in a row. If you fail it restarts it, so don't worry. After this you are told you need to meet the Mad Angels if you had a job at the harbor then you will.

Off to the Harbor. Ask workers you meet until you get some information. A couple of them told me around warehouse 12 at noon (7) you should meet the foreman. I was a little late (12:30PM) and ran back and forth in the area. Just passed the door to warehouse 12, a cutscene kicked in (around 2PM) where I was told I could get a job, I just had to meet the guy outside warehouse 1 (8) the next day at noon. I came back at noon the next day and was told to speak with the guy in Alpha Trading Office (9) by 2PM. I went straight there, and got the job and the trophy.

Unmissable. Please note that once you start working it will be the point of no return. You can never return to Yokosuka in the day time and most shops will be closed after work.