I always loved Nelo Angelo's introduction in DMC1. Heck, Add Phantom and Nightmare to the list as well.
Clock Tower 3 (random choice I know) has some really awesome boss intros as well, especially for the 2nd, 3rd and 4th adversaries.
Oh, and Ryu Ga Gotoku... lots of them. Dynamic intros weren't a thing until RGG3 (sadly, as Kenzan would have head some amazing ones no doubt) but some I love loads are:
Suguichi (RGG4)
Granted there's several I could have picked from 4, but this one is classy and keeps on going right up to the point where you gain control of Tanimura. Easily one of two really good standout moments in the game for me (the second one is with Kiryu not too long after)
Takechi (Ishin)
An absolutely badass fight that starts off really awesomely. The entire fight is full of awesome QTE moments, but I just love how it starts.
Kuze (RGG0)
Yeah the second fight has a badass intro no doubt, but I prefer the raw emotion from Kiryu in this one, as well as how the music kicks in perfectly with the intro card.
And many more to mention. Judge Eyes has excellent final boss intro's (but those are spoilery so I wont list those here), RGG7 has several excellent late game intros once the legacy characters start showing up (so chapters 12 and beyond basically), Saejima fighting a bear, and most recently the final bosses from Lost Judgment (again, spoilers). Oh, and pretty much everything Hokuto Ga Gotoku did. Basically, cant go wrong with any of them in the series!