While the Skyline can achieve 250mph it's topping at 251 over the line so you need to be perfect with it, which is why alternatively i offer you the Pagani Huayra Speedhunters.
Now this car will not do 250 from the off so you need to tune a few things, from the garage menu enter tuning (With the Pagani selected) and change the following:
Front Downforce all the way left to 'Speed' - 0.00
Back Downforce all the way left to 'Speed' - 0.00
Final Drive - 6.00
1st Gear - 2.00
2nd Gear - 3.00
3rd Gear - 3.00
5th Gear - 3.00
6th Gear - 3.00
7th Gear - 4.00
Then save the setup to all tracks, the car can now easily exceed 250mph.
Start any Standing Mile event from the career menu and begin.
Once the lights go green shift into 1st and once the revs are in the green change gear to 4th (skipping 2nd and 3rd) and keep on going normally from there and you should be topping 256-258mph over the line.
The achievement will only pop once all 3 heats have been completed
Here's a video showing you what to expect