after you beat the game do you get to keep all your power ups and tool sif you play it on hard? Also once the game is over is that it or can you go back and get things you missed? 
 
reason i'm asking is because i want to know if i should make sure i get all the riddler challenges before i complete the game or just go back and get them once i complete the game.

So you're asking if it works like the Uncharted games, right? 
 
I cannot answer for sure, but I don't think that happens.

You do not keep any of your items/skills when you replay the game on hard.  You are basically playing a new game.
 
You can however go back and finish all the side mission stuff (joker teeth, Riddler's riddles, etc.) after you beat the game.  It saves right before you final encounter with Joker, so when you go back to get all the things you missed, it acts as if you haven't done the final boss yet.

sweet thank you