You don't need the $15,000 all at once. You just need to accumulate $15,000 throughout the course of playing the game.
I had made around $3,500 playing online co-op with my friend, however, once I reached the $15,000 mark (in solo play) my achievement didn't pop. So, it could be the counter is a tad bit off and it may take more than $15,000 for some people, or it could be playing online (and not being host) has something to do with it. Therefore, don't worry if your achievement doesn't pop, you don't have to delete your save or anything like that. Just keep playing and eventually you will get the achievement, it will just take a bit more time.
A Fistful of Dollars Achievement
Basically, you gain money by blowing up cars and barrels. Killing people actually doesn't get you any money. If you die your money saves, so you could possibly run a part of a mission and purposely die once you blow up the barrels and cars in order to keep grinding money. Since you could potentially grind money in any level, it all comes down to personal preference of what level you want to grind the money in.
Chances are you will be somewhat close to the $15,000 mark once you complete the game the first time, so you could either do another play-through, or you can find a level that has a lot of barrels and cars in it. After my first play-through I utilized "The Betrayal" mission because the beginning part of this mission has a ton of barrels and cars. Run through the first part of this mission as fast as you can blowing up everything and when you get to the part that requires you to take the airplane out of the area just save the game and restart the mission from the beginning.