This achievement is for purchasing new hats/masks in the shop. The early ones are very cheap and if you buy everything in the first 2-3 shops, you can have this achievement done less than an hour into the game. Later hats are $500+ so it's better to just do this quickly.
If you want to save the money for whatever reason, you could also just collect hidden packages and complete side missions. Those hats will most likely count as well.