Qualifications
We get it. You like dolphins. Moving on...
Looking for an entry level job? Let's do a checklist real quick:
Are you over eighteen years of age? Great. High school diploma? Mazel tov. CPR and First Aid certifications? Awesome. Scuba diving certification? Double-awesome. Can you swim? And by "can you swim?" we mean: Are you able to pass the swimming test? The entrance exam for SeaWorld is grueling, and involves a 67-meter freestyle swim, a 33-meter underwater swim, and a 7.3-meter free dive to retrieve a weight from the bottom of the pool (source).
That's just to get your application in the door. If you want to actually get the job, you need both experience in animal handling and some general life skills. Let's do life skills first. The application process at SeaWorld involves a public speaking test (a microphone test, as it's called) to make sure you can put together sentences sure to impress guests. You also need to pass a rigorous and intimidating interview process with the other trainers.
What are they looking for? Experience in animal handling is a killer-whale-sized component. Although you're going to go through a yearlong apprenticeship anyway, you need a lot of experience with large animals under your belt. This experience can come from many places: volunteering at an animal hospital; working on a farm; an internship at an aquarium, zoo, or water park; shadowing someone who works in animal husbandry, etc.
If you love animals so much, you're probably considering an undergraduate degree in marine or animal biology. That will certainly do the trick. However, since you're not just studying animals but training them as well, you should also consider a degree in psychology, concentrating in animal behavior (source).