This achievement is called 'The Chariot'.
Use Zobio and Zobiko to send one hundred Curien Mansion Creatures back to the grave.
You have to buy these pair from the shopping menu. Once bought go to a single race on the Outer Forest track and change the laps to 9. Now the trick is you have to take out the zombies with weapons and drift boost only. Just running into them at normal speed, which will spin you, doesn't count.
Rockets and KO gloves seemed the best weapons. Just line the zombies in your sights head-on and unleash your weapons but don't get too close as you may miss and hit the zombie with your car which will spin you instead. I generally slowed down beforehand to give me more time to take a shot.
All I did was try and kill as many zombies as possible in 9 laps then rinse and repeat the race. I got it on my 6th single race of 9 laps.
You don't have to win the race for the kills to count, just finish the race.
Update 1: Just want to add that there is no in-game tracking of the zombie hits ie under the achievements list within the License menu so just keep doing the race over and over again. Once you hit 100 the achievement will pop.
Update 2: As pointed out by Tallboy2005 (thanks) make sure you turn hazards on cause if you have them off the zombies won't appear. The option to turn hazards on/off is in the same menu where you can set the amount of laps.