Well, this is not something you an accomplish overnight. If your competitor is constantly appearing on TV and being quoted in news articles, it will be very difficult to dislodge him from his “celebrity” status, which was probably extremely hard-won. It's very likely that this lawyer labored in obscurity for years, slowly building his web presence, writing numerous blogs and articles, and sending out press releases whenever he had a successful outcome to a case (or even just to offer his perspective on breaking news stories). This lawyer also probably spent a fair amount of time cultivating the media, by shaking hands at local fundraisers or otherwise being active in the community.
There are two ways to go about building your celebrity status. First, you need to emulate your competitor by building a solid 'brand” presence on the web, which will involve commenting frequently on breaking news stories in blogs and articles, and sending out press releases to trumpet your firm's accomplishments.
Second, you may want to take a cue from this other lawyer by starting to cultivate the local media yourself—your local TV news producer or newspaper editor may not even be aware that you exist, and that you can offer another perspective on local news developments. You don't want to come on too strong—”How come you always call the other guy and not me?”—but a more gentle, friendly approach can work wonders.