It is very much impossible or very difficult to defeat him or, most importantly, kill him in the dream world but it is possible to defeat him in the real world because he has no power there except hand-to-hand combat and whatever he is fashioned with when taken out of the Dream World and into the real world. To extract him from the dream world and transport him to the real world you must be physically contacting him (touching or holding) and wake up while still doing so.r
In the dream world he controls everything and whatever happens in the dream world happens to the person/people in real life. Very few survive the dream world.
Freddy Krueger received control of the dream realm via the Dream demons summoned once he was burned alive.
Whenever Freddy Krueger dies in the real world, he is reborn in the Dream World.