For the black hole achievement, I'm speaking of the ship who shot diagonally. You should watch replay of the #1 in Stage 1 for a better understanding.
For the achievement with the Stage 5 mid-boss, you must reach/beat with a 12x multiplier. I hardly remember what I did because I got it during my first playthrough. I went read the japanese wiki and they said you must have a 12x multiplier at a certain point.
For the train achievement, I also read the japanese wiki. It said the same thing as me that you have to "eliminate quickly the panzer squad". Maybe you can't use bomb. Like I said at the beginning, a lot of things are random in this game and can't be 100% accurate.