The Battle of Britain from July-October 1940 was completely fought in the air (not including British Anti-Aircraft weapons). The Luftwaffe attempted to dominate Britain through the destruction of the Royal Air Force. The British managed to fend off the Germans and maintain aerial superiority. So while not being one side attacking the others ground troops, the battle was completely aerial in nature.

Are you including battles between naval forces

There are hundreds of examples of wars which have been won primarily because of naval power, in which the land portion of the war was happening, but was ultimately not the cause of the outcome of the war. This is completely different to a war in which no land forces are deployed or used whatsoever, which is a ludicrous idea. Even in the example of the US launching airstrikes against ISIS, the ground troops are the Iraqi Army and the Peshmerga, so there is still a land war happening even if airstrikes are the primary means of attack.

A battle is completely different, literally thousands of battles haven't involved land troops, naval battles are incredibly common in war, as are dogfights or airstrikes.

Sorry, we don't allow throughout history questions. These tend to produce threads which are collections of trivia, not the in-depth discussions about a particular topic we're looking for. If you have a specific question about a historical event or period or person, please feel free to re-compose your question and submit it again.