Burnout CRASH!

Short version:

Once you unlocked "The Desert Storm" vehicle (I believe 60 Stars).

Use Desert Storm on the first Road Trip (Windbrush &1st).

4 cop cars appear (GOOD COPS) as the first feature, once they are all damaged a cash truck will appear (considering that you have not let any cars pass in the meantime, othwerwise an ambulance will appear as stated below in the comment section).

Make sure to blow up cash truck (or let it blow up by itself) to cause the three cash bags to be thrown out.

Top left / top right / and bottom right - The Desert Storm vehicle is light so I got the top two bags with the same cashbreaker and the bottom one right after with the second cashbreaker.

Achievement unlocked.
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MONEY BAGS DO SHRINK IF YOU DO NOT GET TO THEM IN TIME - IF THE BAGS SHRUNK ON YOU THEN YOU CANNOT OBTAIN THE ACHIEVEMENT AND WILL HAVE TO WAIT FOR THE NEXT TRUCK / ROUND.
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Extended Version:

I progressed through the single player campaign until I unlocked "The Dust Storm" (60 Stars) vehicle which is lighter and easier to maneuver when trying to get the three money bags after activating the cashbreaker.

Once I had unlocked it I went back to the very first Road Trip (Windbrush & 1st) where you eventually cause the police to block off one side of the road (the first feature - GOOD COPS).

I always made sure to remain somewhat in the center of the intersection because it is easier to control where you want your car to go and not let any cars pass you (if you did miss one or more cars an ambulance will appear instead of the Cash Truck). Ignore the police because cars will just end up crashing into the four squad cars giving you less to worry about.

Once the 4 squad cars have been taken out a cash truck will appear (if you did not miss any cars at the intersection - otherwise Ambulance). Make sure to hit it, but normally it crashes by itself at this point anyway. As it explodes it will make three cash bags appear (one top left / top right / bottom right).

First I went for the top left cause at the time my cash truck had come from the left so I was close to that bag.

I made sure to get the top left and right in the same go, and right after with another explosion the bottom right bag. As soon as I got all three the achievement unlocked.

For those of you who would prefer to see it, here's the video. It is the 1st achievement in the video.

^{Credit to: Rooster Teeth @ Achievement Hunter [Season 9 Ep. 18]}

I got this using the trashmaster and a bit of luck on the first road trip (Windrush & 1st). All I did was to create a massive pile up of cars around my vehicle, then when the bank truck came it crashed and exploded by itself. Once it had dropped the money bags I hit the crashbreaker and collected all 3 with cars I had shot into them, as this counts as a skillshot and you collect the cash to. Hope this helps.

Ok i just found out that the traffic also can collect moneybags for you with the use of crashbreaker! (in my case two bags)
I can confirm that the collected amount of money will be added to your score in order to count (depends on the amount and size of the bags ofcourse)
I wasn't going for the achievement btw i was just playing and saw it happen and thought that it can be helpful to others.
So if the other solution doesn't work out for you, try to combine it with what i mentioned above.