You need to enter a Novice race either in the campaign or in Racebox. The important thing in order to get this trophy is you have to get eliminated by the other racers, rather than simply bumping into walls or doing a barrel roll.
1) Get to low health by running into walls, doing barrel rolls or being hit by weapons.
2) Make sure the killing blow is by a weapon placed by another racer.
3) Win the trophy.