An explanation of the strategy for the Chairman boss fight.
The Chairman
The Chairman will make golden bulls appear and charge downward. You can walk to a safe lane to avoid them. After the bulls stop, the Chairman will charge downward at you, so try to move to avoid this.
Then the Chairman will inflate a golden balloon and throw it at you. You have to bounce it back at the Chairman until it explodes at him. The Chairman is vulnerable to attack after it explodes.
After repeating this, the Chairman eventually starts making two bulls charge at a time. He will jump to the safe lane, so stand under him whenever he moves.
Eventually the Chairman will starts making three bulls charge downward at a time. With careful timing, you can jump over them. It's easier if you have the Spring Boots.
After this, he'll throw a balloon once more, and after it explodes at him, you only have to hit him one more time.
Pick up the money, heart, and Power of Wealth that he drops. Then there will be a cutscene.
Delvin
At this point, if you die, then save and continue, you will start with the Delvin battle if you return to the boss room (you don't have to redo the Chairman fight).
Delvin will quickly move, stopping at either the top, left, right, or bottom of the red carpet. He will sometimes make a circle of purple orbs appear around him which he will shoot outward after a moment. He's vulnerable to attack while the orbs are visible, so try hitting him with the lighter or other projectile weapons. The Fire Resistance Tunic, or Fire Protection Potions, make you immune to the orbs, so you can just walk up to him and hit him repeatedly while the orbs are on screen.
Sometimes he puts tentacles into the ground that move around the area. You can throw bombs at them to make them disappear. He is vulnerable while the tentacles are moving around.
After you have done enough damage, the fight will move to a floating platform where the island is visible below. After some dialogue, the battle continues. Along with previous attacks (now with faster orbs/more tentacles), Delvin has some new attacks:
Delvin will throw his scythe at you a few times. It moves quickly, and will flip toward you at the end of its arc. Delvin can also turn into a black orb, which will dash at you after a few moments.
Eventually the battle moves to a glitched screen, where you can walk off the edge to wrap around to the other side. This is helpful when avoiding the black orb attack, and the scythe. The second time Delvin does the black orb attack, you need to wrap around the edge of the screen to move on to the final phase of the battle.
After enough damage, Delvin will transform. In this phase of the fight, the middle of the bottom of the screen is the safest place to stand. Delvin will make the action buttons spin before throwing them at you. Delvin will do the same with your hearts, which will set you on fire, although you can avoid damage from them entirely by using the Fire Resistance Tunic or Potions, just like with the purple orbs. You can jump over the action buttons and hearts to avoid damage from them as well. Delvin can also send out a large number of tentacles at this time, and can do the spinning purple orb attack as well. Keep hitting him throughout this phase until you defeat him. Congratulations, you won! The ending that you get will depend on what you did during the game. If you got the Perfect Ending, visit the Level 9 page for help with it.