A relative degree will always be useful and do you no harm at all, better off with it than the competion who don't have it!. However in most circumstances in this world, it is who you know, not what you know! Have you had any experience working with animals at all, farms for example? that would be useful. Getting any voluntary work with animals, even only a few weeks here and there will also help. Because no zoos advertise positions that would not stop me applying for a post, find out who is the man or woman in charge and write to them asking for a job interview. It is not pushy, it is proactive and will give you a better chance. If you get no reply phone the zoo you applied to and ask to speak to that person. If you speak to them let them know you are keen and very serious about a career doing that, if you can afford to perhaps offer your services free for a few days. Things like that will make you stand out from the others who want a job but don’t go the extra yard to get one. Going back to the start of my post, if you know any one who knows anyone (etc,,) who works with animals and can put in a good word for you then that will really help kick start things. The money is really poor too for several years at least, so bear that in mind, it was the financial side what stopped my going into further Animal Biology/Ecology research.