For this achievement, all you need is to have 21 stars TOTAL. You do not need to 3-star and particular maps with Original Arkham Batmobile. I just got 21 stars, and the achievement popped right away. I personally cannot decide if I like or hate this Batmobile, as it's handling is rather quite terrible. The good news is that with all of the additional maps now (1989, Tumbler, and 1960's, Batman v Superman) you no longer have to 3-star every race, and can also say goodbye to having to do 3-lap races!
Speaking of the handling of the Original Arkham Batmobile, it seems as if the slightest nudge will send you flying the opposite way. This Batmobile also seems to be unable to explode, and it loves dragging other cars along with it. For your entertainment (and slight knowledge) I have included a video of the fantastic handling of the Original Arkham Batmobile. Please note that this is not meant to be a video guide, just hoping to give some insight on the handling. The video is below:
At this point, you can do whatever tracks you are best at to get this achievement. I only did the single lap races, and I had no issues. Below are the maps you can use, and I have put my results in parentheses.
-Penguin Dockyard (2 Stars)
-Batcave Set (2 Stars)
-Ashes (2 Stars)
-Cataclysm (2 Stars)
-Cobblepot's Causeway (3 Stars)
-Joker Parade (3 Stars)
-Midnight Fury TT ((Time Trial) 2 Stars)
-Cauldron Speedway TT ((Time Trial) 1 Star)
-Crushonator ((Riddler Course) 1 Star)
-Condamned ((Riddler Course) 2 Stars)
-Mental Blocked (Riddler Course)
-Batmobile Proving Ground
Don't forget you can also do some Hybrid Maps as well:
-Seek and Destroy (2 Stars)
I did not even touch the following:
-Penguin Dockyard: 3-Lap Race
-Batcave Set: 3-Lap Race
-Joker Parade: 3-Lap Race
-Ashes: 3-Lap Race
-Cataclysm: 3-Lap Race
-Cobblepot's Causeway: 3-Lap Race
-City Heat TT
-Batmobile Proving Ground: 3-Lap Race
With all of the above, I believe there is the opportunity to earn up to 69 stars, making this achievement much easier than the others.
Hope this helped! Happy Gaming.