I second cave diving as a contender, along with wreck diving and deep diving.
Just as climbing Mount Everest is an order of magnitude more difficult and dangerous than climbing smaller mountains, cave diving, wreck diving, and deep diving are similarly more difficult and dangerous than typical recreational scuba diving.
In fact, one wreck in particular, that of the SS Andrea Doria is often referred to as the “Mount Everest of scuba diving.” Something like a hundred divers or so dive the wreck every year, and to date, 16 divers have died.
There are a host of additional hazards in cave and wreck diving beyond the hazards of recreational scuba diving, including issues with visibility due to lack of natural light, lack of visibility due to silt or sediment, risks of getting lost (and running out of air), risks of entrapment or entanglement, and breathing gas management. Additional hazards with deep diving include the increased risk of decompression sickness, breathing gas management (including multiple gas mixtures), nitrogen narcosis, oxygen toxicity, equipment failures due to depth, and even high-pressure nervous syndrome for very deep dives.
Incidentally, one of the tenets of both cave and wreck diving is to follow the “rule of thirds” for breathing gas management. The rule dictates that one-third of the gas supply is planned for the outward journey, one-third is for the return journey and one-third is a safety reserve. Just as Everest climbers may endanger and sometimes lose their lives by pushing on beyond their planned turnaround time in a bid for the summit, divers in overhead environments have lost their lives by pushing on beyond their planned turnaround point, and finding out too late they did not have enough breathing gas to return (perhaps due to an additional unforeseen problem during the return).
Personally, I started recreational scuba diving again last year, and have absolutely no desire to ever do any cave or wreck diving. I just think the hazards are unacceptably high. (I have no desire to ever climb Mount Everest, either, for the same reason.)