Can somebody tell me what are the dark, wind, and fire things are?

Notice how (most of) the abilities have coloured symbols next to them, Red, Blue and purple? The red ones are fire abilities, blue is wind and purple is dark. To unlock the medals for these, you have to clear 20 missions with at least 4 of that element ability equipped and none of the others. You can also unlock crests that power each up by aquiring 100 silver medals for the dark crest, 103 for the fire crest and 106 for the wind crest.

You need to get a certain number of medals, as C de L said. And for the awards, clear 20 missions with only wind, dark or fire abilities for the wind dark and fire awards respectively. I know this answer is a little late, but I hope it still helps!