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In the The Delicious Last Course DLC, Spoiler:if the player loses to Chef Saltbaker on his 4th phase his quote will be "The mark of my salinity shall scar thy fired glaze!". This is a reference to Street Fighter III: 3rd Strike, where the game's final boss Gill has a pre-battle dialogue that says "The mark of my dignity shall scar thy DNA".
Contributed by ZpaceJ0ck0
In "The Delicious Last Course" DLC, there is a puzzle on the map for Isle IV involving a trio of contest winners towards the back of the Isle and a set of 9 gravestones towards the front of the Isle. Completing this puzzle will unlock Spoiler:a secret boss fight that takes place in a dream world held up by the skeletal remains of the Devil (seen in claymation), where you fight angel and demon variants of the Devil on both sides of the stage. However, they each switch places back-and-forth every time you turn left or right, presumably due to Cuphead's interactions with the Devil in the main game preventing him from seeing an Angel. This boss fight was originally designed as a second phase for the Devil's fight in the main game, but ultimately went unused until the release of The Delicious Last Course. A primitive version of the phase can be found in the game’s data. This boss cannot be refought after beating it. Beating it will unlock the Cursed Relic as a charm as well as the achievement "A Horrible Night to Have a Curse", a reference to the text box seen during the day-to-night transition from Castlevania II: Simon's Quest.
Contributed by MehDeletingLater
Version 1.2 of the game added secret alternate phases to three boss fights, two of which being ideas that were originally scrapped before the game's release:
•Botanic Panic!: Spoiler:By not attacking Ollie Bulb the onion, he will retreat back into the ground and skip to Chauncey Chantenay the carrot's phase featuring an additional mini-boss, a spinning radish named Horace Radiche who despite being completed before the game was released, originally went unused.
•Pyramid Peril: Spoiler:If the player shrinks into the mini-plane form just before the fourth phase of the fight, Djimmi the Great will scan the player and pull up a marionette featuring a dinosaur, a miniature version of Dr. Kahl's Robot and a stone statue, before tugging a longer string and pulling up a smaller version of Cuppet. This skips the fourth phase and goes directly into a harder version of the final phase where the smaller Cuppet will act as a turret firing at the player counter-clockwise to the spinning Eye of Providence pyramids.
•Dramatic Fanfare: Spoiler:By parrying off of the pink star projectiles, the player can land onto two hanging cherub props that control the chandelier in the background of the first phase. Standing on one will gradually lower it until a dinging sound is heard and the chandelier becomes slanted. Doing the same to the other cherub will cause the first phase to abruptly end and trigger an alternate storyline to the fight that was originally unfinished by the time the game was released. After both cherubs are lowered, Sally Stageplay's newlywed husband is crushed by the chandelier. Instead of changing the scenery to Sally's home, the second phase of the fight takes place at St. Timothy's Nunnery, implying that Sally became a nun. In place of Sally's husband worrying in the bushes for her is the Priest that oversaw their marriage, and a Nun takes the place of Sally's children to throw rulers at the player. In the third phase, a god form of Sally's husband accompanies Sally's goddess form and attacks by summoning a cherub, portrayed by Sally's son from the normal second phase of the fight, to push a spinning cardboard fireball towards the player. The fourth phase of the fight is unchanged from the normal path, but with the Nun appearing in the background in place of Sally's husband and children when on Expert mode.

One boss fight in "The Delicious Last Course" DLC also features a secret phase:

•Doggone Dogfight: Spoiler:During the second phase with the circling jetpack puppies, their jetpacks will produce white exhaust fumes when they have plenty of health, with the more damage taken turning it into gray exhaust to indicate that they have low health. If all four jetpacks are spewing gray exhaust at the same time with none of them having been defeated, the Dog Chinook will appear and eat them before grabbing the plane as if it were the normal third phase. However, the puppies and the Chinook pilot will appear in portholes on its paw pads instead of the laser satellites, where they throw regular and pink Pineapple Mint grenades that explode into shrapnel when they are hit. The Chinook pilot also appears and calls for the vessel to shoot homing fire hydrant missiles.
Contributed by MehDeletingLater
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According to animator and designer Tina Nawrocki, Baroness Von Bon Bon's design was inspired by Bebe Daniels, Betty Grable, Loretta Young, and Joan Crawford (specifically her appearance in the 1932 film "Letty Lynton"); actresses who were around during the early 20th century, as well as Marie Antoinette, the last queen of France before the French Revolution, whose execution by guillotine inspired the fourth phase of her boss fight where she throws her own head as a projectile towards Cuphead.
Contributed by ProtoSnake
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If the game detects that the game is pirated, a pitch-shifted and reversed version of the main theme song will play on the title screen. When this song is plugged into a spectrogram, the end of the song will form The Devil in the 3 forms of his boss fight - Regular, skeletal and giant face.
Contributed by KidDivinegon
Found within the game's files is an unused title theme for Cuphead with lyrics. This may have been composed during early stages of the game's development, as the lyrics describe a completely different plot from what was featured in the final game.
Contributed by CuriousUserX90
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According to Jake Clark, when he was designing Cala Maria, The character went through a notable amount of changes before settling with the final design.

Before being settled for having a octopus on her head. Her face originally had fish fins on the side of her face, she had various different types of crowns(along with different hair styles) a starfish was considered to be used at one point, she had a round earring on her nose, a crab tattoo on her right arm, and wearing gloves.

It was also considered for her to hold a weapon(A sword and an anchor). As well the following for her attacks. Cala using her tail, summoning swordfish, a giant crab, and using a title wave.
Contributed by CLXcool
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In the games files, you can find an unused boss based off of a Pachinko machine that goes by the name "Pachi-Pachi".
Contributed by CLXcool
The developers planned to surpass the Guinness World Record for number of boss battles in a run and gun game by having over 30 to the record's 25.
Contributed by DrakeVagabond
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According to animator Jake Clark (who animated most of the bosses in the game), the mermaid boss Cala Maria was inspired by not only Betty Boop, but also Disney's Ariel (for the bra) from The Little Mermaid, and a female moth character from the Disney Silly Symphony cartoon "Moth and the Flame".
Contributed by CLXcool
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In the background of the garden level where the player has to fight the potato and carrot bosses, there's a bag that says 'Acme Grow'. This is a reference to the heavy use of the word "Acme" (an Ancient Greek word meaning "the peak", "zenith" or "prime") as a generic corporate name in media from the silent film era onwards, most prominently in Warner Bros.' "Road Runner and Wile E. Coyote" Looney Tunes shorts.
Contributed by CLXcool