I think I
kinda figured out how to summon that red ship
slightly more consistent, but I should explain it a bit first...
First, a video showing my kusoplay~ 
(
60fps version)
(I guess I should have bombed there, haha...)
OK, some details to discuss further about this.
The translation of the associated achievement in the X360 version goes like this:
"DeltaZeal: At the beginning of Stage 1, defeat enemies from right and left at some timing."
First, you should destroy the very first enemies that appear from the top "fast enough" so that in the next segment, 6 new enemies will appear from the left and right side, not 4 or 8 of that type. You have to shoot them at a specific time frame.
Something I was thinking about (if it had any effect at all or not), is the coloring of the stage background, the clouds. Look closely. If you destroy those 6 enemies at the point when the color of the clouds is a bit brighter than usual, hopefully the red ship appears. This can be examined and discussed further, but I hope that should explain it good enough. It could be either that or some other timing entirely.
I hope this tip is useful for this community.