Dogma (The Binding of Isaac Repentance): In TBOI normally, you enter the boss door, and it shows the boss icon on a Black background with the same boss intro theme. HOWEVER, with Dogma, you ascend to "Home" where you freely walk around until you touch your MOM'S bed, where you get a special floor transition screen, and the whole house turns dark. And once you walk in front of the TV, the doors lock, and Dogma appears out of the TV and lets out a scream that turns the screen white; then the boss title appears, and it includes a Different rendition of the boss intro theme and a static-like background, which adds to the boss aesthetic. (Also, "Living in the Light" is one of the best Boss themes ever, in my opinion)

Sanitized Agent 3 (Splatoon 2: Octo expansion): With all bosses (Except for DJ Octavio, who's basically similar to his Splatoon 1 introduction), it mainly boils down to a giant light coming out of the ink, while the boss slowly rises, and they let out a scream that then reveals their name. But with Sanitized Agent 3, they are at the top of a pillar, alongside a captured Captain Cuttlefish, and then jump down at you with a Splashdown, without any name introduction or scream like the other bosses

(Awesome Trope) Unique Boss Introductions