This Trophy is progression based
This trophy is for getting the title Monster Annihilator for 50 grade points. It is after Monster Abolisher and Monster battler respectively. Simply done, all you need to do is participate in 800 battles, i obtained this around my 35 hour mark in the game.
I'd be honestly surprised if you somehow DON'T get this Trophy in one story run through, you'd almost have to go out of your way to do it. Both random and Boss battles count towards this total as well, all there is to it!