Achievement can be obtained at the hippodrome east of Alexandria (same place for Ben Hur achievement). I think you need to complete the side quests in the area before to unlock it - not sure because i completed everything anyway before attempting this.
For those who didn't manage to do this from the first tries:
- remember that there are no difficulty related achievements
- on hardcore destroying a carriage in 3 laps is close to impossible due to trashy camera and controls
I strongly advice to change it to easy for this achievement and avoid annoying yourself with a poorly designed minigame.
Managed to achieve this on the first try on easy after a frustrating hour of attempting in on nightmare difficulty