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.
You can only earn skips in Extended Play, not live shows, so your first step will be to join an extended play game. Microsoft is currently (Mid November 2009) running an extended play show every half hour in the evenings (at least for United States games, I can't speak for other countries) so this shouldn't be an issue to find.
Next, you earn a skip for answering 3 questions correctly in a row. You can only lose skips by using them, which you never want to do for purposes of earning this achievement. You earn the achievement by earning 3 skips, the maximum possible to hold at one time.
-If you get 2 correct answers, then an incorrect one, your count resets and you have to try for 3 correct ones in a row again.
-Each extended play show lasts a half hour, so you will have around 35-40 questions in which to attempt this.
-Skips from previous games don't carry over.
-If for some reason you accidentally use a skip, it will preserve your streak, but it also won't count towards progress for earning another skip.