So either Faize or Arumat isn't in the party, how can I go about getting trophies for both of them? I know after finishing I can reload and get the other person to come with me, however that doesn't explain how I can get the trophies for both.
Battle trophies are saved seperately from your game progress save. This means they are completely independant of your save. Once you've unlocked a trophy in any single save, it will show as completed in all of them. Nice eh?
However, any partial progress to a trophy is lost between playthroughs, so if you got 1,000 kills one one run through with Arumat and then played through and kept faize instead, you wouldn't still have those 1000 kills counting to the total for Arumat. Each trophy must be completed in its entirety in a single playthrough, including the post-game extras.
Once you've completed the game, if you have a save where you'd normally chose you can simply reload and choose the other person and do their trophies from then on, as the person who leaves your party battle trophies will show as unlocked in your profile anyway.