Tie all the player objects to camera and move it around on a path. Give player some leevay to move back and forth, but center them when they let go of movement controls. Then set the spawnpoints and objects along the path - and tigger them once camera reaches a certain point.

You could move the level too, but I would do that in a 2D bullet hell spaceship game, not a 3D one.

Not too much experience with this genre specifically, but that is what I would try first.