Sonic & All-Stars Racing Transformed

I got this on the Egg Hangar track. To unlock this track I believe you need to complete the "Pursuit" event in the 3rd Tour in World Tour (Scorching Skies).

Set up a single race and choose the Egg Hangar track (Top Row Icon, bottom right track once the icon is selected). Choose Sonic as your character as use the Balanced mod (requires level 2 Sonic).

Shortly after the start of the race there is a massive left-hander. Begin drifting as you approach the corner from the outside and adjust your kart as necessary. Don't worry if you're coming towards the end of the corner, just continue drifting and the achievement should pop as well as an in-game sticker.

All the provided solutions are good. However if you don't want to play that far into the game, this can be achieved on the Studio Scrapes in world 1. You should have Sonic's Cart up to level 2 but you may be able to get it without that. On Studio Scrapes in world 1 the first turn in the race start on the far outside (right side of the track) on the left hand turn and start your drift early and hold right on the control stick to force the cart to do a shallow drift to stay with the turn. You may need to adjust further in the turn and apply boost from the pads the help, but it can be done early in the game.

Try ghost mode with sonic in the Egg Hangar level and the standard mod
When you reach the first big curve start drifting from the outside and use your boost to further yourself through the curve.
THE CURVE DOES NOT HAVE TO BE DONE IN 1 CONTINUOUS DRIFT, you can start and stop more drifts from left to right quickly, but the drifts have to be very close together with almost no gap

You will get a sticker when you get it

You will need to start a race in a map full of turns (like the Egg Hangar map) and you will need to choose Sonic the Hedgehog as your racer. Then you must simply wait until you reach a turn and hold to drift. If you have drifted for exactly 10 seconds, the achievement will pop.

You can do this on any course. But anyway, you can drift by pressing
Note: make sure you go as slow as possible.