For this achievement, you'll have to run 10.000 meters, ride 40.000 meters and swim 1500 meters. My personal suggestion is to make sure that you swim the 1500 meters, and then the 10km meter run and 40km ride will come as you continue in the game.
If you do want to focus on it, do remember that while on your horse, you can hold A and the horse will run on its own, and you can set a marker on the map that your horse will follow if you press y after the horse goes on auto-pilot. I'd also recommend not running with your horse in a city, as it seems to run slower while in a city. I'd also recommend running in a low-level area, like Lake Mareotis or Siwa, since there's a smaller chance you'll be attacked by random soliders.
As for the running, I recommend combining this achievement with the "Overheating" Achievement. Although you don't have to run around in the desert for this achievement, you might as well do it if you're going to be active on it. However, you'll be running a lot in this game anyways, so as previously recommended, just play the game and you'll easily get the 10km.
As pointed out by adcustom in his solution for this achievement, riding a war chariot does NOT count towards the 40km.