Sonic Rush Adventure - Purple Emerald 7 in 0:57:96

Hold the stylus on the screen at/slightly after 1 to get a boost start.
Rings help get to and maintain boost state. Avoid enemies / obstacles when possible.
Avoid jump ramps as they lose significant time - though occasionally they're necessary to fill the boost meter.
Move in a straight line as much as possible, especially while boosting, because moving to the side loses speed - this means use the stylus as little as possible while boosting. It also means it's sometimes not worth moving to get rings and/or avoid obstacles, because the timeloss from that doesn't justify the timeloss from losing speed.
When you must move, moving rapidly seems to lose more speed than moving slowly - this is especially apparent when UNboosted. Of course, you don't want to move TOO slowly which eats into the amount of time you move in a straight line.