Earn 20 perfect Drift scores.
As a rule, during the campaign you will want to avoid drifting since it slows you down around corners. There are some multiplayer lobbies specifically designed for drifting, but the easiest method to earn Sidewinder is in a private multiplayer lobby with one Drivatar.
This is much easier if you set the drift counter to display on your HUD instead of the default lap time. Do this in the Forza Profile screen from the main menu. scroll to the HUD option at the top of the screen and press and then change Drift HUD to ON and press to save.
From the main Forza screen, choose Multiplayer, press to create a private match and to confirm. Once the vehicle selection screen opens, choose a car that is rated B or below. At this point you will be in the lobby, so press to change the options to match these choices:
Game Type: Circuit Race
Track: Indianapolis Oval
Max Players: 2
Max Drivatars: 1
Drivatar Difficulty: New Racer
Collision Mode: Always Off
Car Class: Any
In the assists menu, turn off TCS, STM, and ABS. Choose or rent any fast car that you are comfortable with rated S or above.
You need to hit the corner out of the straightaway at 180mph or above, turn slightly to the left and tap the for the emergency brake. This should put you in a drift, and then it is a matter of drifting long enough to rack up 5,000 points and recovering without touching the wall or the grass. You get two opportunities per lap (other than the first lap where you won't be going fast enough at turn 1) so in a 15 lap race you can attempt this 29 times.
Note that there is also an achievement for scoring 7,000 in one drift (Drifting Away) that you should attempt to unlock at the same time.
Here is a video from OctagonQontrol getting it done: