Fight fire with fire, like the Dilbert character "Topper".
He claims to have climbed a mountain? Say you climbed that one AND took a private submarine to the same depth under the ocean the next day. He says he saw bigfoot? Claim to have worked on the genetic research project that created bigfoot. Did he think bigfoot was a wimp? He should see the chamelion version that never got out of the lab.
UFO ride? You wish you could tell him about the UFO you hijacked and gave to the military, but you're still under contract for... well, *look around furtively* can't go into that here.
The less likely, the better especially if it's just a slightly cooler variant on whatever it is he claimed to have done.