This solution is for using the L.O.G vehicle, but you can use your own with either a flamethrower or the laser.
The event you must race in is the 'Big Rimmed Race Off
When the race starts quickly press
to jump out and
to edit the vehicle, this pauses the race.
Now in this edit mode select the two flame throwers on either side and place them facing forward on top of the two front wheels, now exit the edit and quickly get back in the vehicle to resume the race, you will need to catch up but the AI isnt that hard.
Once near another race press
to use the flamethrower, try your best to spin them so you can hit them side on, burn them until the achievement unlocks.Note: when i completely destroyed a vehicle (all wheels fell off and car collapsed) i did not get the achievement but when i destroyed one wheel i got it when the opponent respawned.
Here's a video demonstration.