You will die a lot!
Glorkian Warrior is the latest from Pixeljam Games and it looks just wonderful. It has elements from Galaga, but it looks like the longer you play the more of a shoot 'em up it turns out to be as you take on procedurally generated invaders.
The game has been in development for quite a while now, and after many experiments and iterations, Glorkian Warrior is now available on the Apple App Store for $2.99. And to quote the PR, "No IAP, no complicated leveling-up systems, just good old fashioned entertainment like your great grandpa used to enjoy." Awesome.