One strategy to implement is: throwing your notable case outcomes in their face.
A good practice is to include such outcomes on your website biography page. Implementing a separate website page dedicated to case outcomes for your entire firm is always a successful practice as well.
Content detailing notable case outcomes can be repurposed across multiple mediums. Aside from existing on your website, this content makes for some impactful social media posts. Type your outcomes up, and place them on an aesthetically pleasing graphic (that conveys your brand colors, of course).
Notable case outcomes are great blog topics as well. These can also be repurposed across social media channels.
Ensuring case outcomes are disseminated is more effective than solely preaching you are the best. You must prove why you are the best.