For this achievement you must spend 5000 coins total, over the course of your campaign against Gale and her pig army. Getting 5000 coins will take some time or take some real world cash. See this solution on this achievement for tips on earning coins:
So feel free to use your coins at any time, just keep note that the game won't let you know how many coins you've spent so you might want to track your own progress. You can spend coins on extra birds, clearing smoke, or charging your hammer. They all count towards this achievement. My favorite method, after getting a bulk of coins, was to just keep charging the hammer power-up to complete a level without using any birds. It is 120 coins per charge, so it went by pretty fast.