One way of getting rid of scraps - indeed, one of the only ways at the start of the game - is to knock them with your finger when they're standing on a tearable floor (one which your finger can "push through" on the back of the Vita system). To get this trophy you have to get rid of forty scraps in this way.
If you get to end of the game and haven't got this, then return to either the first or the second bookmark and play through those chapters (the Standing Stones or the Orchard). Both have scraps standing on tearable floors.