FORECLOSED

Depending on how often you die as you play through the game will determine how close you are to getting this trophy by the time you finish the story. The more you die, the closer you'll be. I know that sounds backwards, but the autosave/progression towards the combat-related trophies is incredibly forgiving in this game, so even if you find yourself dying over and over, ever enemy you defeat will count towards this trophy, period. Go for the other comat-related trophies first, since you'll get at minimum 230 kills from Veteran Sniper , Gravity Bender , and Brain-hacker  alone. Outside of those, you just need the Telekinesis Bullet hits, which will grant you at least another 50-60 kills. 

If you've finished the story and are still short, you can grind these out in the chapter "Bad Trip". You can grind them out in the left or right room, it's up to you, but the left room does have more enemies. Whichever room you choose, clear your way all the way to end of each and allow yourself to get killed by the final enemy. This will reset the room and allow you to clear through it again. 

Once you've defeated your 350th enemy, the trophy will unlock.