* In Star Wars: Episode IV - A New Hope, Luke fires the shot that destroys the Death Star's exhaust port, but he's guided by Han Solo and the guidance of the Force.
* In Star Wars: Episode VI - Return of the Jedi, Luke is aboard the Death Star, but he doesn't directly destroy it. The Death Star is destroyed by the rebel fleet attacking it.
So, while Luke is instrumental in the destruction of both Death Stars, he doesn't personally blow them up.