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Unlike past Skylanders games, the hats you receive from finding and opening hat boxes is completely random. You can even replay levels and open the same hat boxes again to receive a different hat. You can even get the Rainbow Hat by doing this, which is the hat you receive on the console versions by completing the game on Nightmare mode. I'm planning to scan the Rainbow Hat to some of my figures using the 3DS game and then play Nightmare mode on the console.
Best place to get a hat quickly is the Palace of Waking level in the Tradewind Isles area (the fourth "world" you can unlock). There is a hat box you can get immediately at the start (walk towards the bottom right of the screen). Open the hat, then exit to the Eternal Archives (the main hub), and repeat as often as you want to get new hats.
Although there is a retry option while in a level, you need to exit to the Eternal Archives/hub to force a save, otherwise if you just retry the level you will lose whatever hat you just unlocked.
The only downside is the loading time for the level/hub and the intro to the stage which can't be skipped. It's about 45 seconds to start the level and another 25 seconds to get back to the Eternal Archives. So roughly over a minute per hat.
By the way, best hat in the 3DS version is the Gold Top Hat which boosts Health +15%, Damage +15%, Experience +15%, Critical Hit Chance +15%.
Yep, there are 245 hats (at least in the 3DS version). I did this trick over the weekend and now have all 245 hats.
You can get 241 of them through opening hat boxes, but for the last 4 (Jolly Hat, Kickoff Hat, Springtime Hat and UFO Hat), you need to scan the special figures that came with those hats from Swap Force and the Target pre-order card from Swap Force.
Actually, I'm not sure if you can just scan any figure already wearing one of those hats to unlock them, or if you in fact need the original figures/card. I just used the actual original figures/card when I unlocked them on my game.