EDIT AS OF 7/15/10: This achievement is no longer obtainable as it has been announced that season 3 of 1 vs. 100 has been canceled. If Microsoft decides to bring it back, however, I will leave the old solution in place.
To get this achievement, you can be playing in either extended play or a live game. In my experience, live games have easier questions to start, so if there is one going on when you are attempting this, I'd go with that. Otherwise, go to extended play (sometimes extended play has a themed set of questions, so if you are particularly knowledgeable in the area that the theme is centered around, try that).
Next, you are going to need to answer six questions correctly and get the "instant answer" bonus for each of the six. This is easier said than done. You have to be fast in answering in order for the bonus to pop up, and you will know if you were fast enough by a lightning bolt appearing over the lock icon by your name at the top.
Here are a few tips that might help you get one of the harder achievements for this game:
-You CAN use a skip to preserve your streak in attempting this. I personally got 3 correct, used a skip, then another 3 and had the achievement pop. -EDIT- Reading the comments, it appears using a skip in the middle of the streak has worked for some people and hasn't worked for others. I'll update this if any more info related to this becomes available. Feel free to leave a comment if you have any information on this.
-You are going to be a lot better off trying to actually answer the questions than simply button mashing in hopes you will get it by randomly getting 6 in a row correct. The odds of getting it this way are very bad - (1/3)^6 or a little better than 1 in 1000.
-Questions get progressively harder throughout the game, so this is much easier to attempt towards the beginning of a round.
-If you are bad at trivia or slow at reading, try attempting this with a group of people - The odds of someone knowing the answer and preserving your streak are going to be a lot better this way.
-Along those lines, try getting matched up with 3 other people in game and ask if anyone has microphones so you can help each other out with answers.
-One of the previous solutions here said that you can instantly answer incorrectly, then use a skip (on the same question, since you can skip after you have answered) and this will work towards preserving this streak as if it were a correct instant answer. I personally haven't tried this, but there were several comments by people saying it had worked for them. I'm not sure why that solution was deleted, but I thought that information was useful so I'm going to list it here.