Like a lot of shooting games, Super R-Type hates you. And that means that you'll be seeing this a lot.

So, if you want to see the later stages, you either have to spend some time practicing or...

You could go to the Difficulty Select Screen

Hold down the R button and press Up, Up, Up, Up, Up, Up, Up, Up, Up. Done right you'll hear a confirmation sound.

Then, start the game, and pause. While paused press Select, R, and A all at the same time. If you're successful, you'll see a number appear in the lower-left corner.

Letting you select whichever level you want.

Just be aware that levels 00-07 are the Easy difficulty and 11-17 are the same levels on Normal difficulty.

Also, good luck!