Odds of Getting In
You can't just grab the nearest stranger and have them serve America's federal government. In addition to having a clean record and a driver's license, there are some pretty rigorous tests that you'll have to go through in order to prove you have what it takes to slap a federal badge on your chest.
In addition to the online application (for which you can only apply during an "open vacancy announcement" (source), you'll take an occupational questionnaire that'll rate your educational background, training, and prior work experience on a scale between seventy and one hundred.
After meeting the minimum score requirements, you'll then be recommended to take the Special Agent and Test Battery and Writing Sample Assessment. The Battery is a web-based test that measures your reading and comprehension skills. The writing sample portion of the test requires you to write a report based on a photograph provided (source).
Assuming you pass the assessment—which we know you will—you must then make it past a structured interview and then a second personal interview. After that, you'll have to pass a drug test, a medical examination, and background test. We weren't kidding when we said these tests were rigorous.
One of the best ways to prepare yourself for the position (in addition to getting a more advanced degree) is to get some law enforcement experience. Not only will that give you the skills and training that you'll need to pass some of the assessments, but it'll also give you a competitive background.
They want the best of the best, so getting top marks in school is also something that'll set you apart. It's also recommended to hold some sort of leadership role, whether in a professional, academic, or public environment (source).