So I played through all of the game on normal, except for about 5 minutes when I wanted to see what Easy mode was like. Popped back up to normal but because of this I didn't get the trophy. I remember what chapter it was, if I go back and play through all of it on Normal will I get the trophy? Or do I need to play through the entire game again?
Play the chapter on Normal. The trophy should pop.
If it doesn't, complete the last chapter again (and watch the credits), and the trophy should pop when you get back to the main menu.
Either way, no, you do not have to play the entire game on Normal again.