Assuming you have found most of the money stashes, saved the hostages, etc... you may or may not get this on your first playthrough. I was about mid way through chapter 7 when it unlocked.
Any money earned is lost if you don't reach the next checkpoint. For instance, the 25k at the end of chapter 2 will only stay in your account if you finish the mission, if you're killed it will disappear from your account and you'll have to grab it again. Also, you will only get the money from the big piles that are lying around once, but the money from supply crates will count every time, as will the money for objectives.
Feel free to spend your money, the achievement will pop when you have earned $1 million across all playthroughs. You can check this by going to the start menu, going to statistics and looking for "Total Money Found".