1. Do them over hand, or palms out. That way you can use all your back muscles as
well as biceps, and not just biceps as with underhand pull ups. It will be harder at first, but once you develop your back a little it will be much easier.
2. Look up at the bar the entire time. Only pull yourself up high enough to where you can poke your chin straight up in the air to touch the bar. Dont pull yourself up to the collerbone and have your entire head up over the bar, you will save energy this way, thus increasing your reps.
3. Don't come all the way down. Leave a little bend in your elbow and keep tension on your arms the whole time, bust out reps as fast as you can. Be careful, because if you make this too obvious, they won't count it. Make sure it looks good, but don't exaggerate locking out your arms in between reps. The longer you stay on the bar the weaker you become, so do pull ups quick and get it overwith. Until you know your almost exhausted, now is the time to try and squeeze out 1 or 2 more by hanging for a few seconds in between reps. Try changing the distance between your grips on the bar in order to use differents muscles in your back, that usually gives me at least one more rep.
4. Drink a redbull 5 minutes before PFT. The caffiene spike will help you with pull ups. At least it does for me.
5. Make sure the bar has good tape on it on PFT day. You can bring some athletic tape to a pft at your oso station, later at ocs you get what you get. If you have a sticky, solid grip on the bar....it helps. When I was working to get my 20 pullups i would bring my old rock-climbing chalk bag to get a frickin death grip on that bar. I know I'm a geek.