When you're the most bad-ass person to ever walk the streets of El Paso, Texas, or when you're just too intense for everyone. Also can be used plural.
"Hey man look at the ultimate bad-ass show off his car. That fucker."
"We are the ultimate bad-asses, no one can fuck with us.
This is the expression used for the type o' guy who has to pay for repairs on the tank that just hit him, the guy who uses helicopter blades when shaving, the world record holder for most lead eaten in under a minute, the guy who's faster than a crack head with a prescription pad, the very same man that had Chuck Norris mow his lawn, the kind o' guy who catches his taxis by hand and the one we all know as Ultimate Badass.
"Wow! That guy just pimp slapped that polar bear!"
"You mean Stephan? Yeah, he's Ultimate Badass"