I want to become a Marine Biologist, maybe even do mammal training. The university I want to attend only offers a Biology undergraduate degree. Should I go for a minor in marine science and maybe even a second minor in psychology?

A degree in biology is just fine. Minoring in psychology would certainly be helpful if you go into the training field, but not necessary. I do recommend some psych classes though--learning about operant conditioning, positive reinforcement, memory and learning is all useful. My degree was in biology with concentration in zoology.

One of the most important things I look for when hiring is hands-on animal experience. Make sure that you do as much interning and volunteering as you can while you're in school. This will give you great experience and demonstrate to future employers that you understand what is involved in caring for animals.

For a great into to training I recommend reading "Don't Shoot the Dog" by Karen Pryor. I provides a great overview of the basics of animal training.