In the Internet I have found one extreme sport mixing three of the four different categories you have given to us: air, water and mountains. And this extremes sport is rappel. You do rappel in the mountain, it can be close to a waterfall, and in spite of you can think it is not a air sport, sometimes it is, because it depends of the place, you can be held by a harness, with the space on your feet.
The rappel it consist in descend a wall or a vertical surface held by a harness, as I said, being helped by your feet. An appropriate equipment it is required (helmet, harness, good shoes, and comfortable clothes)
I have already done it, in Thailand, two years ago. And I really had fun!!!!!