Walking to the south pole is quite hard, but lots of people have done it. I know the bloke Inge who organises most of the trips, generally it's mentally where people fail. The blind bloke who wanted to do it, made it. Ditto walking up everest 10 times. The "ooh look at me, pay me some money" television people who do "feats" for lots of money and with lots of support? Hmmm, I'd like to see them work in a factory for 20 years screwing the tops on toothpaste tubes for £6 an hour. I suspect they would find that harder.
Doing a marathon in less than 2 hours, or a mile in 3 mins 40, or lots of similar just-out-of-reach-but-theoretically-doable feats in well established sports. That's probably the toughest thing you could realistically try to do.