To obtain the "Last Man Standing" trophy in Shadow of the Colossus, you must get through the entire game without dying.
This isn't as difficult as it seems on the easiest mode, but it is FAR easier if you already know what you are doing and are playing on New Game+, which is necessary to get the Platinum in this game anyway. The key to success is to take the time and grab lots of lizard tails from the save shrines, and lots of fruit from the trees, to heavily buff your ability to see a fight through to the finish. Obviously if you have already been through the game once you will already have a significant buff to your stats as soon as you start.
You can also hit the
button before your death animation is completed to quit the game and revert to a previous save.