Andor Genesis is a big ship that appears at the end of stage four. Start at stage four and progress to the end of the stage. When you get to the first river Andor Genesis will appear. To defeat it you need to drop a bomb on to the dark circle in the middle of it. As soon as it appears head to the right side of the screen and try to get close to it while dodging the shots. When you're in range drop the bomb to defeat it. Just keep selecting stage four in stage select and you'll get it eventually.
taken from http://www.xbox360achievements.org/game/xevious/guide/