It is a pretty straightforward achievement. Play on Overkill solo or with players and when you get the bags of money, the fastest route would be going from to basement to the kitchen area that leads to the reception like area where there is that one dude always behind a counter, from there move up to the second floor and all the way to the bag deposit point.
Having bag movement and bag throwing skills will speed up the the process.
NOTE: You do not need to get all of the bags. I played solo on Death Wish and got only 12 bags out of 16 and I still got the achievement.