This one is self-explanatory. The game isn't that much harder without upgrades, but the bosses will pose a scarier threat with your limited ammo capacity. Make sure you aim for headshots on the Haunted. Failing that, legshots. Collect trap parts - i love me some bolts. And remember that tapping X will regain stamina really fast. Stamina was my main problem with this run - remember to release the button before it depletes or Seb will be eaten/beaten before he catches his breath.
The 100 gel you're required to upgrade in Chapter 2 doesn't affect the trophy.