For this achievement, before the race, set the following options:
Difficulty: 1
Damage: Visual
Assists: (All should be off)
ABS: OFF
Racing Line: OFF
Stability Control: OFF
Auto Steer: OFF
Corner Braking: OFF
Trottle Management: OFF
Automatic transmission is fine, as is the full HUD. Using flashbacks is also fine. Now just run the race, and the achievement should unlock assuming you won.