To report this colleague?

She's speaking to you this way because a) she's not a nice person and b) she thinks she can ie she does not feel you have a sense of authority to you. This is something for you to work on because if she sees you this way then others will too.
I am guessing you are a nice person - I mean that in a nice way - but you need to find a new groove where you can remain nice but also give off a sense of authortity. When you say something to her, she's snappy at you and you then apologise when you didn't do anything wrong. So she is perceiving you as weak.

If you say something and she replys snappy then give her a short reply in an abrupt tone like "no one said you are stupid I have been told to train you and that's what I am doing'... and then walk off.

As difficult as this person is being - she is going to help you in the long run as its clear you need some work on your confidence.

Correct her every time and document your corrections via a follow up email. If it continues with no improvement then escalate to her line manager. Keep it purely factually with the evidence to back it up. Don’t correct her mistakes as this means she’s getting away with it.

Just read yku are not her line manager. Why is her line manager not reviewing her work? Not sure s/he can line manage her if she's not reviewing her work. Pass the reviewing to line manager.

She's still on probation. E mail any errors. Once. If she repeats then that's on her. Or tell whoever that the training is not going well, someone else can take over.

Document EVERYTHING. The mistakes, what you said, what she responded with.
DOCUMENT. EVERYTHING.

You're being apologetic for her mistakes - why?

Literally painting a target on your back. Just be calm and factual and stop feeding into it.

If you’re not talking to her like she’s stupid, then don’t apologise for doing so. Just say ‘I’m not intending to make you feel stupid, I know you’re new to the tasks but it’s really important that we get these things right for clients.’

I like this suggestion. I was going to say that she may be used to a more direct approach in the workplace and possibly has construed your attempts to soften corrections as patronising. However, I'm very surprised that as a new employee still in the probation period she feels comfortable being so rude to you. That isn't a good sign.

You need to address this directly with her. Every time she makes a mistake raise it with her. Keep a record ... date/time/issue/response (do not put any names on this).
Stay very calm and state the issue precisely and ask if she needs any further help/training. Ask her to confirm she understands the issues raised.
If she snaps ... youve two choices ... ignore or ask her not to respond in such an unprofessional way in future as you are just doing your job abd you dont expect to be spoken to in this way.

agreed...
I'd err on the side of caution and not even repeat the word she used like stupid... because she could quote you "I'm not calling you stupid."

work on some counteracting phrases..... "I would never use that word to a colleague."
"Please review the items I've highlighted for you."

And report it all.

I also liked the breezy pleasant "Good Morning Name" as you go past. She wants a reaction and to hurt you.. so being seemingly unconcerned will thwart her.

Consider her training complete. She's as trained as she's ever going to be. Any mistakes going forward are on her and that's for her manager to deal with.

Please don’t apologise if you are not in the wrong. What does she learn from this? Her unreasonableness is rewarded. Go on the offensive whilst maintaining absolute professionalism. Something like ‘Oh! How would you phrase it then?’

Stop apologising. When she starts that, say something like

“do not talk to me in that tone, I have not called you stupid, I am simply pointing out an error that needs to be rectified for the future.”

Why do you have to fix her work? Is it your job to check her work? If it’s wrong give it back to her to fix!

She has a bad attitude and is bullying you. Don't stand for it, take a more assertive approach i.e. 'I know you aren't stupid but it is my job to train you and that is what I am doing.'

Remain calm, consistent and firm in your stance of ensuring she learns to do tasks correctly.

If she doesn't like it - tough. If others can see that she has a big chip on her shoulder - good.

I was in a similar situation OP. I was working with someone who, if she liked you, was nice, if she didn't like you, boy did you know it. She'd be so unpleasant, people stopped going to her for things that were actually her job and do them themselves.

She hated my guts, no idea why. I tried to talk to her twice about it but nothing ever changed. So I want to her manager and basically said either you deal with her or I will file a grievance against her for her behaviour. She got spoken to and things vastly improved when she realised she would not get away with speaking to me like crap. I would have filed it too.

Agree with the other comments. Fully detail in writing what you have trained her in and when. Perhaps send it to ask if she needs any recaps or anything more and cc in her line manager
and then email her with corrections Every time but dont fix them yourself
With regard to what she is saying as yoj walk past that is just childish but I know it does get to you. Try to ignore it but always walk past with a breezy :good morning" "goodnight" so she can't accuse you of completely ignoring her.

I agree with the person who said have your phone switched to record if she makes mean remarks when you walk past.

But check if that is legal first.

It's awful having to work with someone like that. Although you are keeping a written record, try not to let her get to you and never respond in kind as it would only be used against you. Your best defence is to remain calm and professional but reporting.

Do you have a union? maybe report your concerns so that they are on the record and you have extra advice.

Have some neutral prepared phrases up your sleeve to counteract her when she says things like don't call me stupid...

"I did not say that. I was simply asking you to make some corrections."

"I don't name call because it is unprofessional. Please make the corrections I've highlighted for you."
"That was never my intention."
"can we please focus on the corrections"

ask her to correct mistakes by email and blind copy in her manager. Don’t let her get to you. There’s often one of these types in every work place in my experience . Learning to deal with them is a discrete skill of its own.

Also don’t apologise to her when she snaps at you!! She’s relying on putting you on the back foot! Report all of this behaviour including her being even more nasty when you’re on your own with her and also record her even just the voice if not audio to show hr what you are having to put up with

Speak to her line manager and ask them going forward if it would be a good idea to keep them in the loop with the work that needs to be reviewed. Do you think she would be making these mistakes if she knew her line manager needed to be copied in to the work she has supposedly completed?

I would follow up with an email and also ask at that point "would you like further training on that aspect of the job"

This records that she has already had training
offers further training

it covers your back

you don't want her complaining that you didn't train her on something after she has done it wrong after that incident

Presumably, if you’ve been asked to train her, there must be certain training/performance objectives that she has to meet - can you give feedback to HR against those?

If you haven’t been given any objectives, then you need to ask for some!