All codes are done on the Title screen, where it says "Game Start," Password," and "Sound Test."
To start from Stage Two, hold R on Controller 2, then press Start on Controller 1.
To start from Stage Three, hold L on Controller 2, then press Start on Controller 1.
To access the Bonus Mission, hold L and R on Controller 2, then press Start on Controller 1.
This will only work if you score 4500 points or more in Missions One through Eight.