After going through all four seasons, which is the introductory part of the game, you'll qualify for the Horizon roster and also unlock the respective achievement. Upon doing that, the drag strip will also be unlocked and a new event will be available just to the west of the Horizon Festival, titled "Horizon Festival Drag Strip."
By going to the Autoshow and pressing
, you can filter out the cars that are not eligible. Scroll down and select "Hot Hatch", then press
.
The selected type needs to be "Hot Hatches" specifically and not another hatchback type, like "Retro Hot Hatches" etc. Then you can press
to sort the Hot Hatches by Class. The better stock car of the bunch for this achievement is the Audi S1, which comes with an AWD drivetrain, offering a nice launch off the line. Buy that and then head to event.
It's a drag race, so obviously you'll be racing in a straight line. The achievement will pop if you manage to cross the line with a sub-25-second time, which is pretty easy with the stock S1 and it doesn't matter if you win the race or not. If you're still struggling for whatever reason, you can just auto-upgrade the car to the next class or search for a basic tune I've shared to the Storefront, using my Gamertag or typing "hatch me if you can" in the description.
EDIT: Make sure you don't create a custom Blueprint while going for this one, since it doesn't count towards it it seems. Use the default one for Hot Hatches instead. Thanks to users "A Volvo Driver" and "Borg561". In addition, it appears it only works in Solo.