To get this achievement you have to run for 25,000 meters in Endless Run, in a single run (i.e. you cannot do two 12.5KM runs to get this, it has to be a single 25KM run).
Note that using the Extra Life power-up is allowed (but it's pretty expensive, so...). For me it took a dozen or so tries before I got it -- the best trick I found is to roughly memorize the left/right turns you took, as even in Endless Run the obstacles will always (or at least, very often) be the same for the same left/right turns you take. I also used the keyboard, not touch, to get this. I find the touch controls slower.
The achievement will unlock once you die.
If you have any tips/tricks, please leave them in the comments and I'll update the solution!