Devil May Cry

Sounds like Mission 17.

Slash back the skeleton dragon's fireball back to it three times (think it's only once if you're in EA mode - can't remember) to destroy it -- time your sword slash when the fireball is about three quarters of the way towards you. After that, turn the nearby crank until a cutscene is triggered, pick up the Quicksilver, then go back into the corridor, turn off halfway down, and use it on the red door.

Air Hike is the quickest way to reach the Quicksilver, but if you don't have it, jump onto a ledge and use the invisible platforms (they show up during lightning flashes) to get there.