I personally did this on the Interchange map, however any of the Tier 1 (Easy) maps should be fine. You'll need to play until you have saved up $50,000 all at one time, so spend as little money as possible. I got this trophy around wave 13. Helicopters will spawn around wave 6, a juggernaut will appear around wave 9. You should get the trophy before the next wave of special enemy units appear.
One of the most important things to remember as you play is that you should keep track of the streaks in the bottom left-hand corner. When the bars fill up you will get significant cash bonuses. Some streaks that can earn these bonuses are headshots, consecutive kills without being hit, and knifing killstreaks.
Take your time; don't try and play Rambo-style, its just going to get you killed. Your main strategy should be to maintain some distance between yourself and any enemies. This will allow you to retreat if needed. Preferably you'll just scavenge weapons from fallen enemies. The only items you should buy are ammo refills and flashbang grenades for the juggernaut. This trophy is fairly easy, especially if you've played the campaign on Veteran, just don't expose yourself unnecessarily and keep an eye on the radar to keep track of where enemies are.
After you're done with this, use the money you saved to earn the Danger Zone or Defense Spending trophies if you are at a high enough rank to have unlocked everything.