Well, there's a lot of them... But getting them before completing the game would be a bit of a pain. For example there's one for 100 link battles, and I don't see a reason to force myself into battling 100 times before I finish game.
Also doing 1,000,000 exp in a day is possible before finishing the game, but it's much easier to do it at battle tower - in my case I got it without even knowing it exists...
If you want to you can look trough list of medals and see which are possible before finishing the game. It'll probably be something around 150. Then if you're so inclined you might do a challenge to get them all before finishing the game, but frankly "getting them all after finishing the game" is already good enough challenge.
Oh, and to maximize your medals you would probably want to finish elite four with only one pokemon, which will be dual typed - it will give you "One and only" medal, and 2 of "defeat the elite 4 with only one type of pokemon".
Oh, or another one of those "you might not want to do it before game, but you can if you are going for this kind of challenge" medals - the one that requires you to do 1000 street passes :) --- PSN: TheAreinu (BFBC2, BlazBlue, LBP) White 2 FC: 0047 2018 4094
You can not get all medals before E4, there are medals obtained in Black Tower and White Treehollow, and those areas can not be accessed before E4 --- 3DS FC Ares 3738 0446 1787 <> Black 2 FC Enyalio 0562 4621 2772 DW Collection: http://tinyurl.com/3qz7odk