You will need to know your address. It can be found in your apartment, in a letter on the counter next to the sink. The address is randomly picked from a list, but follows this format:
_00 _____ St.
Apt #454
___, __ _____

PASSIONATE WORKER
Type up 100 entries total.

DEEP THINKER
Every time you are sent back to your apartment, interact with all objects: Fridge, letters, notices, packed boxes, couch, bed, door, window, bathroom mirror. You don't need all of them for the achievement, but it couldn't hurt.

HARD WORKER
During the 5th session you will be transported into a path that ends in a large, circular pit with your computer on the other side. Rather than jumping into the pit, carefully creep around the circumference until you can step off onto your desk. Stand in front of the computer and interact with it to get the achievement.

CONFIDENT WORKER
Don't delete any mail unnecessarily. This can be accomplished easily by never using the delete function after it is given to you, or only using it once it is necessary. When S U B M I T appears on the screen during the finale.

USB DRIVE
Obtain the USB drive by continuously following the instructions of the mail directed to Data Conversion Operator, which you should send to your apartment's address.

SCRAPPER
Interact with the scrap of paper found on the floor next to the shelves in your office during the 4th session.

VOYEUR
Mail yourself 20 letters. This isn't hard to do if you spread it out across multiple sessions, and/or mail yourself as many letters as possible in session 1 before you're given a warning from your manager. After the warning, only mail yourself a few letters, letters addressed to you, or letters that have no highlighted text.

SAFE & SOUND
Progress through the game, following the instructions in the letters addressed to you, the Data Conversion Operator. During the finale of session 6, send the letter referencing you (it will have your name and address) to your apartment's address. What a neat souvenir!

RESEARCHER
Discover all of the letters addressed to a former Data Conversion Operator by identifying the address with which your apartment shares a city/state/zip code, and then sending all of them to your own address instead. Be careful not to get fired.

SIN EATER
A letter will show up on your screen detailing sin eaters. Transcribe the highlighted text, and you will be mysteriously sent home. While I'm not exactly sure what causes the letter to show up, I received it while having 3 curse sticky notes during my 5th session, on my 6th playthrough of the game. It may just be random chance, as I've seen someone get it on their first playthrough.
UPDATE: Multiple people in the comments have said that this is achieved by allowing the power to run out on applicable days. Thanks for letting me know!

EXTINGUISHED
Fail to complete your tasks within the time limit. The game will close itself, and upon opening it again, you will be unable to do anything until you close out the game and re-open it, upon which you will be brought to the score screen.

POSSESSION
Progress through the game, ignoring the letters addressed to you or throwing them away when prompted. Type and submit everything highlighted on the screen.

WITHDRAWN
Progress normally through the game until session 3, when the power goes out and you are put on a timer. Allow the timer to run out. The next day, allow the timer to run out again.

FIRED
Send a bunch of mail to your own address during session 1, then ignore your manager's warning and do it again in session 2.

MAIL BOMB
Sometime during the 2nd session you will receive a package. It's a brown, bulging envelope with 8 United States postal stamps, black tape, notes such as "DO NOT XRAY TAPE INSIDE" or "FRAGILE", and typos in the address. Send it to your home address, and open it the next day despite your best instincts to get the achievement. This will end your current playthrough.

SUNSHINE
Send all the letters addressed to you, the Data Conversion Operator, to your apartment's address and follow their instructions.

EXPERIENCED WORKER
Achieve all endings listed above.

If you've read this far, thank you.
Thanks to Belief Engine for an awesome game!