Mario-like skitting / delecration animation?

Are you asking for errors or just feedback?
Original Mario has a much harder deacceleration that makes him turn faster while yours seem to be more floaty, if you make him stop quicker it will be much more similar. How to do that is impossible to say since we cant see your code.

Basically you'd just be changing the run animation to a brief skid animation upon changing direction. So if player is facing right, then presses left, change run animation to skid. That's how I'd go about it. There might be other details to refining it, but that's the basic idea.

What are you using as movement?
Basically the animation should play whenever the player speed is positive and you're holding left, or negative and you're holding right