Try to use the situation as a way to gain inner strenght by being better than her and not reacting. Pray for guideance when she starts "pushing your buttons"
You talk as if she is [censored] on him and he is meant to be silent and let it pass. That is a very non kahanist attitude.
ItalianZionist said she is just getting agitated. That is fine, let her get agitated.
I don't see why if she gets agitated, it should push ItalianZionist's buttons. Unless he seeks nice relationships with everybody. If somebody is a bad person then you don't have to seek peace with them.. This is all very unkahanist behaviour.
The problem is that as a trainer, she gives feedback to my manager...and with her disposition, it may be negative feedback..Other workers have told me that she wants to make the other workers look bad so that she can look like the "best" worker.
is there equal likelyhood that she will give negative feedback regarding other workers too?
If speaking to the manager, you could pick the safer option and instead of talking of a problem with her, take the unassertive route and act like you are unsure whether you can ask questions (personalise it a bit so he can see you have some grasp of the thing and are thinking about a certain area in an intelligent way). As part of that lack of boldness, only discuss it if he asks you how things are going. Perhaps not unassertive, but at least, it's not bold..
Since you are in the position of learner, I don't think appearing a bit unassertive is such a problem.. And you certainly won't look like a complainer. If you only bring it up if he asks you how things are going, and then you bring up the issue like that.