Thanks for posting this, I didn’t get to answer all the Q’s on the chat today. Sounds like you are interested in science which is fantastic.
To be honest, you could do this with pretty much any science degree with a biological basis. I did a degree in Biotechnology and as part of that I got to do my final year research project in a cancer lab. Most third level institutes and universities have some cancer -related research going on, it would be just a case of seeing what is available and finding a way into the right lab.
For research in cancer it is important to have some understanding of several branches of science (that is what you get in your bachelor degree) including immunology, molecular biology, microbiology, biochemistry, pharmacology and genetics although it would be impossible to be expert in all of these. After that you can take that knowledge to the next level via some postgraduate research in a cancer lab.
Here’s a link to an Irish Times article which last year featured Science as a career. Have a read and if you have any questions even after this competition is over, then you can email me anytime on email@example.com