To earn this trophy, you must shoot at a specific cave entrance way that's shrouded in darkness, and "kill" the darkness.
The darkness will have a health bear and will have the name "The Darkness." As far as I know, it doesn't attack you, and when I earned this trophy it had very small amounts of health/defense.
You basically just need to find it and shoot it.
Note: Only the person that kills The Darkness will earn the trophy if you are in a co-op game You can find The Darkness in the 'Hatred's Shadow' area. On your way to the castle, you will pass a broken bridge on your right. To your left there will be an open entrance to what is known as 'The Pit'. Pass this entrance and you will come to a dead end.
From what I've read, using Magic Missiles grenade can open the door by killing the darkness with it. It would make sense considering the source video that inspired the trophy. Getting into the room isn't a requirement for the trophy. Simply killing The Darkness is.
In case anyone is interested, "That One Video" that's being referenced in the title is referring to the video below.