This is only
an alternative solution in case your game doesn't respawn the hat (even if you didn't complete the level and you just started the game (not much progress). Do not use this method if you are still progressing through the story or story related achievements.
When I attempted the reload method after getting the first had then going back to the menu, it still counted the hat as being retrieved. Since I only needed story-related achievements left and didn't start them yet, I used this method which worked pretty well.
What I ended up doing was hitting the select button on the game's menu hub and then scrolling up to my name. If you click on it, you have the option of hitting to erase your game's progress.
I then launched the first mission and the first hat (banana hat) was at it's location. I retrieved that hat and immediate went back to the game's main menu hub, hit select and repeated until I got all 10.