There is no reason why you can't get this by just working your way through the story. I unlocked shortly after completing 'The Crocodiles Jaws'.
SWIMMING TIP: As this is the manageable number of 1500m, just keep a rough estimated of how many meters you've swam (If you're swimming towards an objective just take not of what the distance started at when you dived in, and finished at when you came out). I did it to 2000m to be safe
RUNNING TIP: Any distance that is 300m or less I would run to. Takes a little bit longer but that way you know you're adding up towards the 10,000m.
RIDING TIP: Finally ride anywhere that is more than 300m away. This map is huge and the story takes you to most of its corners anyway so racking up the 40,000m should just come with natural progression.
Until you have this I would swear off fast travelling unless its across water and you know you already have your swimming metres.
This will unlock at random times for random people depending on what you had left to do. For me it was the riding. Once you've ticked all three boxes the achievement will pop.
BOOSTING HINT: Asides from the obvious rubber band trick, for the riding portion you can set yourself a waypoint on the farthest corner of the map connected to your land mass hold
to make Bayek follow the road and walk away.
Let's keep cheevin' together!