This trophy is unlocked by simply completing the game. This shouldn't be overly difficult since dying returns you to a checkpoint with full health while maintaining any progress you made. This means that any switches triggered, enemies defeated, or boss health removed will stay that way while you start fresh. It costs you time, but you should still be able to slog through.
There will be only a few areas that are tricky because of timing requirements, but since it doesn't cost you much to fail, you should be able to push through.