Fighting against the True Final Boss (at the time before Update 2) Scott Cawthon is basically this, and it's all backed up with an amazing theme. Is it a bit scary because of the concept? Yes. Still awesome because of it? Yeah.
In Update 2, being able to finally kill Chica's Magic Rainbow is an amazing moment in of itself because it's not only a really hard boss that's under a time limit, but it's a huge payback after the endless taunting the rainbow gave you in its minigame.