Is there a way to get pictures of bosses after defeating them?

You will have the opportunity to purchase the missing boss pictures from Symin at the Ancient Hateno Tech Lab. They will cost 500 rupees each and will only be available after you beat the game. Just look for the Elite Enemy Picture set when buying pictures.

There's no "New Game+" as of yet but your saves will have a star next to them once the game recognizes that you have beaten the game.