There's only 63 roads on Fortune Island, and unlike the main game there's few clustered areas like the stunt park and beaches. So spotting where you've been or missed is much easier. No random House driveways either.
The best way to do this is to play the DLC races etc until around level 5 of the Treasure Map main quest/story series. That way you'll get most of the roads without needing to drive them specifically for this achievement. Then, use Fast Travel (which ideally you'll have for free by hitting all the boards on the mainland) to pick off any remaining roads you've not hit.
Often it'll be the end or just a small corner of the road that you missed. Make sure you zoom in on the map as it will show in grey any of those you're missing, with red/white for those you've already covered.