Both Star Wars and the Atari 2600 came out in 1977. You would think they would be a match made in heaven with tons of Star Wars games coming out on the Atari. However, while there were a few Star Wars games that ultimately came out on the 2600, they all came pretty late in its life. Death Star Battle was only the second Star Wars game released for home systems.
As Atari 2600 games go, this one isn't bad but it also isn't anything special. The goal of the game is ultimately to destroy the Death Star and there are two stages. In the first stage you must fend off TIE Fighters while trying to exploit a hole in the energy shield of the Death Star. Once through the shield you progress to the second stage in which you must shoot at various parts of the Death Star to clear a path to the reactor. Then once the reactor is destroyed you must survive the resulting explosion.
In addition to the Atari 2600, Death Star Battle was also released on the Atari 5200, ZX Spectrum and Atari 8-bit computers. Gameplay is similar on all version but the Atari 8-bit and Atari 5200 versions have the best graphics. I don't think this game has been part of any compilations or otherwise re-released so you will have to track down an original (or use an emulator) if you want to give it a try. The Atari 2600 version is probably the easiest to find and it is close enough to the others in terms of gameplay and graphics that it isn't going to make a huge difference which one you play.