N achievement in Portal 2 like Portal’s Transmission Received

Theoretically you should be able to clear Portal's local cache and then it will either have no achievements at all (locally -- Live will be fine) or pick up the ones from Live, I'm not sure how it works. But yeah, clearing the Portal data off your XBox's HDD should allow you to get the achievement again. I've never done this on XBox but I have done the equivalent on Steam.

As ChrisF stated, it's at the beginning of Chapter 7. When you exit the previous chamber you'll see a door to an office on the left, shoot a portal on to the wall next to the door and one in the hallway up ahead. Go into the office and there's a portrait of Caroline and Cave Johnson in there. Stand in front of it for a second and you should get the achievement.

If written instructions aren't clear you can look at this video:

Good Luck!