“Overcoming the World” means having a spiritual focus instead of a temporal focus. When I turn to Heavenly Father and the Savior to help me I overcome the world. (The spiritual world has all solutions.)
Jesus Christ said:
These things I have spoken unto you, that in me ye might have peace. In the world ye shall have tribulation: but be of good cheer; I have overcome the world. -John 16:33
Christ overcame the temporal world by giving his life to go to the spiritual world. When I turn to what’s spiritual (Christ), He gives me peace.