How can one get a settlement for a whiplash injury?

It all depends. Technically there is no such thing as a "fair" settlement. If you were truly injured....not make-believe (like, what treatment did you receive? If it was by an MD rather than by a Chiropractor? How much damage to the car?)....then your medicals and lost income (wages) are evidence. Add pain and suffering. Then think in terms of doubling or tripling that amount... But as I said, it all depends, as there are so many variables.