When you get to the level "The Crack of Doom" you will need to topple Gollum into the fire below. To do this, you will need to use speed attack to get him to the edge of the crevice. When he pinwheels his arms, use physical attack to knock him over onto the edge, then press R2 to attack him with your finishing move. Continue this process five or six times. On the last time, a cutscene should play of Gollum falling into the lava underneath, thus destroying the Ring.