I was an climbing arborist for many years. You don't need a degree or certification to get started. It is a very physically demanding job, and there is usually lots of turnover. If you can get a job with a tree service you would start working on the ground dragging brush to the chipper, moving wood, and raking up. If you stick with it you will learn as you go. Any decent employer would have an International Society of Arboriculture Certified Arborist study guide and would encourage you to take the test. I think you need a couple years experience to sit for the test. It takes a couple years to become a good climber. There is lots to learn: tree identification, tree defects, diseases, climbing knots, rigging, chainsaw safety/maintenance, how different wood acts when it's cut, how the same wood acts at different times of the year, how your employer/customer wants the tree pruned, and how that matches up or conflicts with your knowledge/ethics.
It's a lot of fun, and once you are good at it you should always be able to find work. Anyway, should be easy enough to get your foot in the door somewhere and see if you like it.