If it were me:
I would email her directly and be sure to include a read-receipt. Give her 3 days to respond. If no response, email her again. Wait 3 days.
If no response to the second email, I would print the email and mail it to her via certified letter. I would then send a 3rd email indicating that since you have emailed her twice with no response, you have sent a certified letter. I would end that 3rd email with a three-day deadline date for her to respond; indicate that if she doesn't respond in 3 days, you will lodge your complaint to her superior.
I would also be sure to attach the photo/video and Internet link in ALL emails and correspondence.
NO typos or grammar errors. A professional, business letter.
Since she is the person who is responsible for all decisions at the gym, I would not ask to speak to her boss, unless of course she fails to respond.
I would view this as the first step of a process. Keep in mind that this person that I'm recommending you email was likely responsible for enacting the women's-only policy to begin with.
She will likely either ignore you or defer you to someone beneath her or above her.
I agree 100% about NOT meeting her face to face. Don't do that, in my opinion. Keep everything in WRITING so that you can keep everything DOCUMENTED.
If you end up meeting face to face, let her know (don't ask) that you're going to be recording the meeting via your cell phone, strictly for documentation. Then take out your cell phone, put it on the table in clear view, press play, and proceed. If she refuses to allow you to record the meeting, smile, stand up, say, "Not a problem. I'll just convey my complaint to you via email. Thank you for your time." Then leave. Be polite and respectful about it.
I'll again emphasize the importance of documenting. It's a very effective way of getting people to take you seriously. If you do choose to meet face to face--or if she requests to meet face to face, it is VERY important that you document every word of that meeting, and that you immediately follow up that face-to-face meeting with a read-receipt email, recapping what was discussed and the outcome of that meeting.
Here's one way that I would word a follow-up email from a face-to-face meeting:
"
Dear______:
Thank you for meeting with me today and for agreeing to record our discussion regarding my formal discrimination complaint regarding the women's-only gym hours at the University of Toronto.
To recap the record of our meeting, I explained that_(you could quote from page 4, sections 6 and 8 here)____________________ and you responded by saying_________________. It's clear to me that we disagree about the women's-only gym hours, and I can respect that.
Please feel free to respond to this email by ___ a.m./p.m. on ___________ if you have any additional comments or clarifications on this matter, as I am taking the next step to resolve this issue by lodging the same complaint, along with the comments you made during our aforementioned meeting, to __________________ on the date of ___________.
Thank you for your time."
I'm going to take awhile before I help you draft up another variation of a complaint letter. I'm a bit perturbed now and want to wait before I think of how I can help draft a formal complaint. I don't write well I'm angry!
Maybe some of the other guys will chip in some ideas, too.