With some practice it can be done. I've been able to consistently beat it without a game over, but not without dying at least once.
Unfortunately I forgot to pause and take a picture after defeating the Joker. But here's a pic from when I recently beat it after losing one life. http://i.imgur.com/tyOblpi.jpg
I think this game might be easier to conquer than "Ninja Gaiden" because you can keep using re-spawning enemies to refill health if you screw up. The only real sticking point is the Joker, and you have to do some tricky jumps.