For this discussion, I'm interpreting "athletic performance" as a running event. Almost all other sports are team sports, and exceptional performances on the field are very often the result of chance. (See mario lemieux five goals five ways)Running / track and field is the purest sport there is, so the greatest athletic performance would come from there. It should also be an accomplishment that will likely never be broken. Beamon's jump was great and all, but it was eventually broken. The same can be said of all current world records.That said, I agree with Average_Joe and think that Secretariat's Belmont-winning run is probably the greatest athletic performance. His record over 1-1/2 miles over dirt still stands to this day. Yes, Here is another possibility, there are other animals faster than a thoroughbred race horse, but they can't run around an official track and compete against each other, which racehorses certainly can. No horse will ever match Secretariat's performance at Belmont that day.The second greatest athletic performance ever? Again, likely something that will never be repeated. I like Paavo Nurmi's two gold medals in the 1924 Olympics within 30 minutes of each other. The modern modern games has done better at staggering the distance events so runners can double if they want, so this performance won't likely be topped either. The only consecutive events that still conflict with each other are the 400m and 800m, but only when one is the final and the other is the semi. I would accept a 400m Olympic win and an Olympic record in the 800m semi in the span of an hour as a comparable performance in the future (as the schedule is currently).
Here is another possibility wrote:
A two week old pronghorn would have destroyed Secretariat - probably could have run the last quarter backwards and still won.
Pput that pronghorn in the starting stalls at the 1973 Belmont Stakes and I doubt it would know to run across the finish line.