This isn't a walk in the park. I'd suggest playing on hard if you played the main game on hard, the only real difference I've noticed on this DLC versus the main game is the over abundance of cops, they are everywhere and are quick to spot you.
Playing on Easy you earn just the points per mission.
Playing on Medium will net you a 50% bonus on top of mission score.
Playing on Hard will net you 100% (double) mission score.
It's possible to 1,000,000 on all difficulties, but you'll really have to bring your AAA game to stand much of a chance for the casual/average player on Easy.
Tips for completing the millionaire:
String combos. That's the best way to do it. By headshots, killing, or blowing up cars (demolition bonus). Try your best to keep that bar and multiplier active (top right, next to the green mission clock.
The best advice I can give is this; load up on ammo before car missions, then after you've got the car at the destination DO NOT press X, but get out of the car and blow up the cars around you, stringing them together, you can net a very tidy bonus doing this, I've improved all of my scores using this method, and I'd suggest finishing off as many missions as you can by 'car demolition'. The cops will come, but they don't shot AT you until you either kill a civilian by explosion/shooting, or a cop, then it gets messy, but you can kill them anyway. They don't add to the multiplier though, so bare that in mind if you start going all cop killer :)
Leave yourself a safe 5 'minutes' on the green clock to get back into the car and hit X straight away.
The last 2-3 story missions should net you a tidy amount, in the region of 150-250,000+. I consider myself as an about average gamer, I played through on Hard and finished the game on 854,000. Just using the car multiplier method on the car jacking ones, I'm now just 21,000 short. So that really does make a massive difference, if you do that for story missions as you go, I'm sure you'll get the Millionaire achievement without this need of replaying missions.
The Lost in Transit mission is a gold mine for car destruction, but I'm just not good enough to not die/blow myself up. You can go off, do the initial bit then when you're at the safe point, don't press X on the silver house, go blow up cars trying to maintain your multiplier. There's a handful of players with well over 150,000 on that mission alone.
The Don seems to have high scores too. I was just pleased to finish them on hard at all, let alone attemptint anything 'fancy' to boost my score :)
Hope that helps, any further tips posted in comments, I'll add to this.
Edit: probably very late to this party, only just turned on email notifications, but here's a vital inclusion from
MitoticActivity"Good guide. I would suggest editing the last portion about the city score. If you have 1 million individually in either the story score or city score the achievement will pop. But the scores from story and city cannot be combined for the 1 M"