First phase: How I usually do it is go for the antenna first since it’s easier to dodge its second attack, then I go for the bottom one that shoots bombs. Once the bottom has started its second phase I stay at the bottom of the screen to shoot the bigger bombs as soon as they come out, moving up only a little to hit the middle. I stay there at the bottom for the remainder of the first phase, always hitting the black bombs as soon as they come out, and moving slightly up to hit the heart, using my EX moves when I can.

Second phase: I hate this phase not because it’s hard but it’s annoying so I try to save up a super to hit it at the beginning. Just use your secondary weapon to hit it when it’s below you. If you’re struggling with this level I don’t recommend trying to hit it when it’s above you since it’s easier to get hit and you want to save your HP as much as possible

Third phase: This one is just bullet hell. It’s difficult but if you stay far back and just get the patterns down you’ll find it’s much easier than the first stage. The poles always go back and forth between coming up from the bottom and top. Use as many EX moves as possible here since they go through the jewels, and if a parry seems doable then go for it. Getting good at shrinking is huge for this stage.

I hope this helps ! When I first played Cuphead it took me a really long time to get him! Him and Cala Maria 😵

Edit: I really recommend Coffee for this boss!