Thanks for the reply! As you say, back when I was planning for my BA I didn't take courses that are typically BSc pre-requisites in Canada. I actually have looked into distance education options and found an online school with all the necessary credentials that allows me to learn advanced functions, physics, chemistry and biology at the 12U level from home. I'm looking into whether calculus and vectors is something I'd definitely need or not. But anyways, I can take care of all this during my next summer break, and it's also drastically cheaper than the equivalents offered by universities. In fact, I'm not even sure I could get in to university (at least reliably) for a BSc without first taking care of these high school requirements.
The things is, by the time I've done all this I'll be more-or-less done my BA, and so I figure I may as well wrap that up and not throw my current majors out the window before getting into biology. I have heard about some universities not accepting students for second undergraduate degrees though, as you said - that's definitely something I should look into more. I'm currently attending York University, and I'm planning on moving on to the University of Guelph for my next bachelor's.
Also, I've heard a lot about people entering into graduate school programs without an extremely similar undergraduate education. I know very little about the details as an undergraduate, so maybe somebody could fill me in, but would that really work out for me? I mean, a BA in psychology and history, and then pursuing a master's related to biology? I worry that I'd lack the expertise and the academic profile to even stand a chance, not only getting accepted but with regards to the quality of my studies even if I did.