Ok, my favourite shmup on all systems is
on the C64
It really is my all time favourite, although it may not be the best shmup I have ever played, because I have played a real lot of shmups on C64 and Amiga. I thnik I have at least playtested once at least 90% of all Amiga shmups, and I have finished quite a lot - some being very good ones, like Apidya, Silkworm, Menace, Starrush, Wings of Death,....
But Katakis ( C64 ) surely was the one I was most hooked to.
In fact I was quite disappointed when I saw R-Type some time later. Katakis is similar to R-Type, but much faster, plays better, and also has 12 levels instead of only 8, each featuring a nice endboss
It surely was one of the best games of it's time ( 1988 ) overall.
And it was made by 'Turrican-Master' of C64 games programming Manfred Trenz
ps: Katakis on the Amiga was by far not that good as the C64 version. It only had 6 levels instead of 12, was much harder and grafical inferior.
But nevertheless, I finished it, too, although it must have been one of the hardest Amigagames I ever played thru !