As mentioned above, you have to play each team at least 4 times. First, through the bronze, silver, and gold matches, then, once you complete bronze-gold in a region, the platinum medal will appear where you have to play "jambots". These guys are severely cheap mofos that will have you rolling your eyes on more than one occassion.
Here is what I did/who i used to get this. I needed someone high in steals (like 9 or 10) and someone who was high in dunks/blocks. There are quite a lot of combos that will meet these requirements, but my two favorites are stockton/malone in Utah and Clinton and Obama on the Democrats.
Stockton/Malone: Stockton has either a 9 or 10 in steal and a 10 in pass. he also has a 7 in 3 pters. Malone has a 10 or 9 in the block and dunk categories and also has an 8 or 9 in 2pters.
My recommended strategy is to first try to steal with Stockton and then use malone when they try to dunk it. On offense use the pick/push to free stockton for a 3pter.
I used these two exclusively until i started losing here and there. Which leads me to my next and best choice:
Clinton/Obama:Clinton is much like stockton except he has a higher block percentage. He has a 7 in steals (good enough to steal on most people), but most importantly he has an 8 in 2 pters and and 9 in 3pters. Obama has a 9 in block and a 10 in dunk. he can also steal on most people and has an 8 for 2pters and a 7 for 3pters. So either one can hit from long range (VERY IMPORTANT), and Clinton has a good enough pass to alley-oop to Obama. Obama is your shot blocker. Plus, there's just some great satisfaction seeing a former POTUS and our current one dunking ferociously on your oppoenents. This was an added bonus for me.
Offensive tactic: As I said these jambots are cheap cheap cheap. Unfortunately Clinton/Stockton is not very strong so when you start with the ball you have to run away from them and use a push/pick option. then have Clinton/Stockton run around and towards your hoop. Your big should be trailing and you should send him for an alley oop or to pick/push the other opponent. Then you either fire a 3pter or pass it to your dunker for the alley-oop.
Rinse and repeat. And always try to get someone on fire BUT NOT AT THE EXPENSE OF A BASKET. Trust me, it's better to get the 2pter than to try to line up someone to go on fire. Also, it's ok to take long 2s. Both of these teams have a high percentage inside the arc (unless you're fading away). Run a bunch of pick/push so that the jambots don't block you.
You will have to play at least 120 times and playing the jambots can get a little boring. However, if you can handle the jambots, then the beastie boys are not even worth discussing. You should have no problem with them. They appear after you've obtained all platinum medals in all regions.
Obviously there are other teams you can pick...but these are the main two that i used. Please leave a comment as to the ones that you like.
fyi, you can purchase stockton/malone in the jam store once you get a silver medal in utah and the Democrats I believe are 5000 or 10000 credits. To pick them you'll need to hit RB to see all the "hidden" teams that you've earned/purchased.
EDIT 6/4: I must say that while playing online my Obama/Clinton Combo has been beaten more than I would like (still a winning record). Larry bird and ray allen, however, have been unbeatable. You can even use rajon rondo to steal the ball for you and larry legend will take care of the rest. that's the combo that I'm using now to get the "Arena Vet" chevo.