Sonic & All-Stars Racing Transformed

I found this achievement easiest to get in the first Battle Race you come across in World Tour on C class, I believe it's the Roulette Road stage of the second World Tour (Frozen Valley). The trick is to hang back in last place for the entire race picking them off as the opportunity arises with triple ice shots or fireworks, even firing your blow-fishes forward works well.

You're safest at the back and you just have to watch out for them trying to lob things back at you, but they're far more aggressive when you're ahead. You have 3 laps to hang back and pick them off so you have plenty of time. If you get hit at all just restart. Achievement pops once finished.

Contrary to doing this in World Tour mode, I was able to do it in a Custom Game - Local. I plugged in my 2nd controller(required if you're doing Local). After hitting Local, go to Battle Race and select Ocean View since it's a short map. C class is your go-to option here. The AI don't keep up with you nearly as well as they do in World Tour, and aren't nearly as aggressive, so halfway on the first lap you can easily have a good lead on them if you use the boosts and drift around the corners.

Using this method, your goal is to finish the 3 laps while being no-where near the AI and to avoid getting hit. Once you get your lead on them, maintain that lead until you cross the finish. I didn't encounter any AI trying to shoot me with ice or rockets, however this is random and your results may vary since there's no control over what they get from item boxes. I haven't seen either drones or Swarms while playing Battle Race(at least on C class) so neither of those should be a problem. Your 2nd controller, if left idle, will end up losing lives since the map is dynamic and it pushes them forward. This is fine, it doesn't affect you in anyway. After you cross the finish, you need to wait 30 seconds before anyone who doesn't cross the line gets DNF. Once those 30 seconds are up, your achievement will pop if you were not hit by anything.