There are 18 different Challenge Medals to be collected. There is a 19th one also under the 'Challenge Medal' category, but that one is only available once you get all the other Challenge Medals. xD
17 of these 18 medals are to beat the league with your party being only one particular type. The medal that is not part of these 17 is to try beat the league with only one Pokemon. And then, of course, there is the 19th one which is only obtained through collecting all the other Challenge Medals.
Hope I helped. :)