As you match the gems quickly there is a combo counter in the top left hand corner. Once it hits 15 - 20 it will begin to fill in orange. It will completely fill with 10 - 12 more matches and you'll enter 'blazing speed mode. (The board is now surrounded with flames and the clock stops for a brief time)
You need a combo of at least 15, then you need to speed up. (at least 1 match per second or faster). If you fall behind the bar will drain quickly and you'll need to start over. It's important to note that the blazing speed bar (the combo counter filling in orange) is separate from the combo counter itself. You can have a combo of 40+ without entering Blazing Speed.
Not much I can suggest by way of tips I'm afraid. Abuse the hint button, but try to match gems away from the suggestion first . If a chain reaction starts move the cursor elsewhere and keep matching as quickly as possible. You'll need quick reflexes and a good bit of luck. Use the back button to quickly reset the board if you screw up and just keep trying.
Good Luck! --- It won't be exciting unless we're betting. Besides, like hell I'm going to be exercising with no incentive or reward in sight. - Yukari Tanizaki