How to unlock the achievements related to hidden areas in Portal 2?

Most of the hidden areas I can think of off the top of my head are achievement related (so the below might count as spoilers to some folks).

Specificially, the areas associated with Final Transmission, Ship Overboard, and Portrait of a Lady.

Portrait of a Lady

Beyond that, I know of two easter-egg rooms, the first holds the Turret Quartet, and the second is the secret developer commentary room (with the beeping screeches that, when translated, talks about the Devs involvement in the ARGs).

Turret Quartet:

Another one: the band The National recorded a song called Exile Vilify specifically for this game. It can be found in one of Ratman's dens, in Chapter 2, Chamber 3:

My answer assumes a certain knowledge of the game and of the levels...

Most of these achievements are explorational achievements where you would normally discover them by just exhausting the limits of the test chamber... I am old school pixel hunter and would slave over every pixel of a game to find a heart, bag of gold, or some little easter egg... So portal just made me feel like there was a huge hidden stash in every wacky chamber. Especially the retro lab levels. The videos do a much better job than my explanations.

Door prize

The vitrified doors are located in Chapter 6. There are 6 doors total. They say vitrified on them and you have to go up to them and press X to activate a voice response. Even if they don't open. The door bell like button accompanies each door. You should notice them all around this particular chapter. They don't help you get anywhere... But they all have the moon-rock painted surfaces near them or there is a way to launch/jump to get to them.

Ship Overboard

This one is also in Chapter 6. It's a small life buoy you have to find. It's outside of the room above where you get potato GLaDOS, there is a door in back left corner that will open up. Go all the way back, and out onto a catwalk with a safety gate... and you will get the Achievement.

Final Transmission

You get this Achievement in Chapter 2 - Test Chamber 6. Take the radio that is in the garbage, to the Rat Man's den.

You've got to launch vault to the trash release button. GladDos will dumpa lot of junk...

Once the trash makes it's way to you, one of the items that drops down on the lower level is a radio.

Put your portal back at the start point. and head back with the radio.

Shoot a portal on the angled wall to RECEIVE you holding the radio and put the exit portal on a wall that launches you directly into a abandoned looking damaged wall that has yellow walls.

Carry the radio over to the desk.

Portrait of a Lady

This is in a little nook near the exit of chapter 7's propulsion gel test.

Also an explorational find. It's a portrait of a LADY with the crazy boos man that is hanging on an interior office wall. You walk up to and look it, and it unlocks the achievement. There are a couple of walls you put portals on and it's easy... but also easily overlooked...

Party of Three

This one is a co-op game based acheivement by two people viewing companion cube in chapter 4 Test chamber 9

This involves a series of transport tubes and light wall/floors.

Both players need to ride along together towards the end of a long dark hal and a garage style door will open up in the side wall and a companion cube will appear, simply passing by it unlocks the achievement.

This video shows the level in detail and explains the process. I can't find the screens of the xbox game in sequence to accompany a better explanation.

http://achievementhunter.com/archive/episode.php?id=3149

GameFrontDotCom posted a video showing all Rat Man Den locations:

Some of the Rat Man Den locations are not shown on videos from other answers.