I work for a big consulting firm. In our proposals to clients we provide a "fun fact" about ourselves. In the last three proposals I've claimed to have canoed around the UK, wrestled a bear for charity and be selected as an astronaut for the European Space Agency. Nobody checks.
You can lower the bar or heighten the bar. For instance, claim that once you ate a whole 20 ounce steak in one hour. Or that you personally were responsible for burglarizing the Watergate Hotel for Richard Nixon under an alias, but what you were after was their stash of porn.