If you're not familiar with Showtime, it's entered by pressing LB+RB while free roaming. This will make your car "crash," and you can then control it as it flips and careens through traffic. Hitting A will consume some of your boost meter and bounce you off the ground so you can keep your momentum going. Each vehicle you hit will increase your score and fill your boost. If you come to a stop on the ground, your boost will quickly drain, and if you're stopped with no boost left, Showtime is over.
The only way to increase your multiplier is to hit buses. The main strategy here is to conserve your boost as much as possible, because depending on your luck with vehicle spawning, it may take a while to find ten buses. If there are no buses around, rely on your momentum as much as possible and minimize use of boost.
The other guides recommend Chubb Lane. Webster Avenue is also a good place to work on this achievement. On the section just north of the parking garage, there are usually two buses parked, and buses regularly spawn along Webster and along nearby 7th Street.