This is by far the biggest grind of the game. If you purchase coins with real money, this shouldn't take too long. After your purchase, just buy everything in the Gadgets, Clothing, Jet-packs and Vehicle Upgrades sections to get the trophy. Utilities aren't necessary. The counterfeit machine and the 1,000,000 coins pack are really the only things you should spend real money on as they are the best value but these aren't available in every region unfortunately. Also, some people appear to be having issues with not receiving what they buy after purchasing a microtransaction on the PlayStation Store. Be cautious with purchases.
If you want to not spend any money, I highly recommend that the first upgrades you buy when possible to purchase are Coin Magnet and all six vehicle magnets. These bring coins in close proximity towards you and that's extremely useful. Don't buy utilities unless you have to for a mission. Other possibly recommended gadgets for money making are Gemology, Flying Pig, Flash and to a lesser extent, Token Gift, Magnetic Tokens and Free Ride. After purchasing these, feel free to move on to anything else. Sometimes you'll need to purchase a certain amount of gadgets before having access to the next one so go for the cheapest ones first.
You will need 640,501 coins to buy everything in the game.