Is it possible that you made a deathwarp? Gain a life after losing your last life will warp you into the next level. Example run with this exploit: https://m.twitch.tv/videos/53077027

Explained: In Contra III, defeating a boss or losing all of your lives cause a screen fadeout transition. During this transition the game checks to see whether or not your character is alive. If you are alive you are advanced to the next level. If you are not, you are taken to the game over screen. The programming assumes that the only way to be alive during a screen fadeout transition is to have defeated a boss.