The bad news about this achievement is that it's a lot more than the $1 million achievement. For this achievement you will need $1,555,200 earned (excluding the cost of purchasing the cars, so add a little more for that - I can't check original prices anymore)
The fastest way I've found to earn money is to replay Career Mode -> A Class Plus -> 06. Takedown and you will get just over $1000 per few minutes, but if you hate this gamemode, the races won't be much worse. You can also increase the difficulty in Settings -> Gameplay to increase your winnings per race, but this is only worth it if you actually are winning each race easily.
There is another semi-AFK way to earn money. It is a lot slower, but I found it easier as I could watch Netflix while doing so. Basically you turn on the same takedown race as above and let it time out. You should get $450-$550 for it, then just click retry every 2 minutes. If you are doing this method, make sure to put highest difficulty in settings.
This is still going to be an insane grind, so be aware of it. Here's my calculations just in case I got something wrong.
1 upgrade: 100+200+400+600+800+1000+1200+1500+2000+3000 = 10,800
4 upgrades: 10,800 x 4 = 43,200
3 cars: 43,200 x 3 = 129,600
1 upgrade: 300+600+1200+1800+2400+3000+3600+4500+6000+9000 = 32,400
4 upgrades: 32,400 x 4 = 129,600
3 cars: 129,600 x 3 = 388,800
1 upgrade: 600+1200+2400+3600+4800+6000+7200+9000+12000+18000 = 64,800
4 upgrades: 64,800 x 4 = 259,200
4 cars: 259,200 x 4 = 1,036,800
Total = 129,600 + 388,800 + 1,036,800 = 1,555,200