Although there's not really any need to grind this as it will likely come through natural play, if you really want to get a potentially annoying achievement knocked out ASAP, then this can be done pretty much as soon as you gain full swappable control of Evie and Jacob.
Looking at your map, you want to head south-by-south west until you reach the familiar shape of the clock tower which houses Big Ben. Just east of that is a bridge which spans the full width of the River Thames.
Stand at the Westminster side (west side) of this bridge, and hijack a cart - preferably a police one. Now, head across the Bridge to the east, hitting
to whip up some speed, and pull alongside the smaller, open carriages going in the same direction as you, in the lane nearest the outside bridge wall.
Push toward them with
to ram into them, using
to control your speed, making sure you don't just speed past them after the first hit. After two to three hits (about 5 or 6 seconds) the carriage will tip over, and you'll get a notification in the bottom left corner of the screen. You only need to have this go to 20 for the achievement.
If a police carriage pulls along side you, hit
to jump onto the roof of your own, parkour across to it, and jack it with
. This gets a tough vehicle out of your way, and gives it to you!
Make sure when ramming the carriages that you don't go past them and come back from the opposite direction, as more often than not if you allow them to go off the bottom of your screen they'll be replaced by an undamaged one. So rotate your camera accordingly to keep them in view!
Using this method, going across the Bridge over and over and wrecking 2-3 carriages per run, it took me less than a half hour.
You can also combine this with the achievement for jacking police vehicles.
Great tips from the comments:
"This can also be combined with cargo hijack & cargo escort achievements since hostile carriages would also spawn along the way. "- Imaginary Ruins
"If you are stuck on 95% like I was, unplug xbox from internet -> delete your save from console -> complete first two missions -> ram some vehicles -> quit the game -> plug xbox back online -> choose CLOUD save after the title screen -> select continue and achievement should unlock. Hope it help anybody. P.S.: Don't hate me for my English." - LAS7 WeemaN
"Easiest to use a Fire Brigade carriage." - KarlEmpson
"Mine was stuck at 95% for a long time, until I started the Jack the Ripper DLC. I rammed one vehicle and it popped shortly after" - Marc Cohn
"I unlocked this and fell victim to the "Done! Unlocking..." issue. The achievement didn't unlock, even after the update. I started the Jack the Ripper DLC, and after I destroyed one carriage (police), it unlocked." - burtondude33
Please leave me feedback for negative votes, thank you