I'm going to point out my co-worker's mistakes to our supervisor
Why would you go and point out their mistakes?
She did a mistake and never learns from her mistake
Your boss may appreciate you snitching on your co-worker, but you'll lose the trust of your co-worker and destroy the company morale. You should instead go to the co-worker and offer to help them so that they can be as productive as you are.
She needs to step her game up.
If you really feel like she needs to step her work up, then you should help her out and show her what she's doing wrong.