Batman on NES Defeated (Better Time)- Chris Beats NES Games
So I found for the 2nd to last boss on the last level. If you use the wall to jump over the fireball, while then coming down from it and using the boomerang helps to dodge it a few times enough to beat the enemy.
With Joker also jump off from the wall to avoid the first shot, or first two shots. Then if you get over to joker, it seems like if you start punching him from behind him, instead of directly in front. Then the lightning strike and the gun doesn't tend to get you as much. And you get more hits in as the joker is trying to turn around.
These two things really helped in doing the final bosses in the game. That and making the smallest jumps possible in going through the last stage. While making the biggest jumps possible on the final boss on the last stage.