There are 900 total battle trophies, 100 for each playable character. For all the "per battle" trophies, such as consecutive hits or exact damage, you will personally have to do the action. For some of the larger accumulated ones, such as fighting a certain number of battles, those can be worked on by the AI. However, to actually force the trophy to unlock, you have to use that character personally in battle (some require that you end the battle in control of them). For instance, I never used Faize until the second boss battle, but at the end of that battle I got two trophies for Faize for completing 50 and 100 battles.
A nice way to work on some of the more technical trophies is to return to an older area and set everyone to manual control, then use whichever character you need so the AI won't screw it up for you.
Concerning Faize: you won't have him the entire game during your first playthrough, but on any subsequent play (so long as you do a "clear data save" at the end of your first play) you can choose to keep him in your party instead of taking on the new recruit during the story.
A full list of the trophies can be found here
. A walkthrough with tips can be found here
. This achievement can be worked on over multiple playthroughs, but each trophy's individual stats will only be on one save file. For instance, if you need to kill 100 enemies, you can't kill 99 on one save and then 1 on another to unlock the trophy. All 100 would need to be killed on the same save file. Once you did that, the actual trophy will move to any of your other save files though.