Yep, it's the infamous cuphead Speedrun challenge, but in Unleashed instead (this can work for Console versions too for all I care)

For more info here: https://gamebanana.com/threads/226601

Just thought it would be funny to make a category specifically for this.

would the s rank requirement entail that you get the s rank on the first attempt, or can you replay stages and complete the run as long as you have all the required s ranks?

I think replaying the stages can be fair.