In the "secret area" Quistis gets all emo and tries to tell Squall about her feelings, getting fired as an instructor, etc. but he doesn't want to hear it (and honestly, neither do we). After the dialog head back out of the secret area, then keep heading left around the circle. When you get to the fallen tree you'll hear someone crying for help. Head over there to find the woman from the Infirmary under attack by some flying beast. Here's yet another boss fight!
These monsters don't have much in the way of HP or damage, but they do have some fantastic magic that you're going to want to stock up on. From the big flying guy, Granaldo, stock 100 each of Blind and Shell. From the smaller ones, Raldos, stock 100 Protect. Shell absorbs damage from magic attacks and Protect absorbs damage from physical attacks. After you've drawn all you want, kill all of the monsters. They have no weaknesses, but their health is not very high - 1,500 for Granaldo and 300 each for Raldos.
This woman, again, seems to recognize Squall and Quistis, but they don't know who she is. Yet more intrigue and storyline that will be revealed later in the game.
Leave the Training Center and head back towards the dorms. Along the way you'll run into Zell, who informs you that you now have a sweet new room. Inside, Squall goes to sleep. When he wakes up, he's informed of his first SeeD mission to timber. At this time, go over to the desk and pick up Weapons Monthly April, then save your game.