Established in the Old Republic year of 1845 and modeling itself after the success of the Zaloriis Imperial Military Academy (ZIMA), the Naval Academy was established on Prefsbelt IV mostly as a way to confuse people. Since the Prefsbelt Psychiatric Academy was already there, Republic officials hoped that the Naval Academy would be sufficiently camouflaged by any would-be hostile military force that might desire to destroy it. The tactic obviously worked, as it was never destroyed. Republic officials were pleased.
In 1841, a group of mischievous ZIMA cadets were trying to create a libation that they could use to get chicks from nearby colleges drunk and then bang them. The drink was a fruity, bubbly blend of weak-ass nonsense, but they hoped for the best. They brought their creation to the dorm of one of their girlfriends. Turns out, it was actually a big hit with some of the guys in the dorm, who happened to be seamen of the Republic Navy on shore leave. These seamen were intrigued by the ZIMA cadet uniforms and their ZIMA beverage, but professed that they didn't have what it would take to apply to the Academy. Instead, they petitioned the Republic to establish a Naval Academy, so some of the more effeminate people in the galaxy might still have a chance to serve as officers in the military.
So, in 1845, the Senate officially christened the P4NA open for business. Immediately, it was filled with cadets (called "midshipmen" because they enjoyed being in the middle of other men while on board a ship) who were just as intelligent as their ZIMA counterparts, but had a strong affinity for Bette Midler albums, and a tendency to dress like Liza Minellli. In an attempt to increase discipline, officials hired lots of instructors that would yell out "I want some butts!" a lot.
SportsThe P4NA was a lot more lax in its standards than ZIMA. Because of this, a lot more lazy people wanted to go there. Also, after Top Gun came out, everyone thought becoming a "naval aviator" (Navy slang for pilot) was the greatest thing ever. They were wrong: crushing things in a tank is a lot more fun. But it did mean that a lot of athletic types wanted to go to P4NA and play shirtless volleyball. Since this wasn't a school-sponsored sport, they had to do other things. In the end, this boost in popularity allowed the P4NA to compete with ZIMA, and even surpass it, in most sports competitions, which was kinda lame. They also adopted YMCA and In the Navy as their official fight songs.
P4NA was very successful for thousands of years. It should have been a prime military target for enemies of the Old Republic, but it survived unscathed over the millenia. Prefsbelt Psychiatric Academy, however, was destroyed by orbital bombardment many times, and actually invaded a couple of times. Also, P4NA got an incredible number of applicants that were clinically insane, but they were admitted because the admissions boardmembers were too busy having sex with each other. Because of this, many of the top thinkers in naval history were nuts.
Admiral Motti was a famous graduate of P4NA. But his admission to the Naval Academy was accidental, as he was actually supposed to be a patient at the Psychiatric Academy. This wasn't discovered until Wullf Yularen noticed him smack talking a Dark Lord of the Sith.