At the top of the "player column" on the game screen, right between where your score appears and where your gamertag/gamer pic is showing, you'll notice that it says "Speed" and across from that, "0". When you start making quick, consecutive matches this number will increase by 100. If you get the number to 1000 and continue making matches you'll start to hear a burning sound. At this point, you need to keep making quick matches for about another 5-10 seconds in order to enter "Blazing Speed" and unlock this achievement. (Also note that if at any time you make an invalid move OR take too long to make your next match, your Speed will drop back to 0 and you won't have enough time left to enter Blazing Speed long enough to pop the achievement).
I found the easiest way to do this was to play Classic and just start making 3 gem matches right away - as soon as the round starts (i.e., don't waste time at the start looking for the biggest and best match). When first going for this, I had reached 1000 and the "burning sound" a number of times and kept it up til the round ended and still no achievement. Once I started focusing on matching right away, I hit the burning sound earlier and ended up popping the achievement with about 5 seconds left in the round.
Also, use the 1 or 2 seconds you have while a match is being cleared away to look ahead for your next match - it can make all the difference in keeping your Speed up and preventing it from resetting to 0.