What is incorrect about my answer? hmm?
You can NOT convert a png file into a vector file. Your method certainly isn't a conversion plus using the trace tool is problematic having to constantly undo and repeat because it either over traces or skips parts.
When using the pen tool its a one time trace that's very easy just by clicking points over the original artwork. If you don't like my answer that's fine make you're own but do not lie and say its wrong when it isn't.