Leviathan is the final boss; he appears after defeating the 35th level. He follows an exact pattern without any variation, and you can let green IonBall's go without losing a life if you happen to miss them. What made this somewhat of a challenge, for me at least, was that I had upgraded my paddle size to full length already. This made dodging his laser attacks more difficult. These attacks bounce off the walls which make it hard to judge where they'll end up, but if you pay attention to his pattern you can minimize damage.
Here is the pattern Leviathan:
[From Level Start] Far left, then middle, far left again, then middle, stay middle, to the right (underneath boss, hit boss with ball), after the blue lasers go quickly left-center, stay at left-center when he shoots red ball, stay here again (underneath the boss now), back to the middle after blue lasers (you can hit the boss here if you launch the ball then quickly move to the middle, but it's risky and not recommended), stay middle while he shoots red ball, repeat to start.
^Sounds like a lot to learn, but once you play the boss a few times you learn it quite easily and this pattern I described makes more sense.