There are four powerful fairies in the game, and they can all upgrade a part of the armor. At the beginning each of them is magically trapped in a bud and you have to give them a certain amount of Rupees in order to get them out. As you free the fairies, you can subsequently upgrade the armor (up to level 4).
Note that with each new fairy the cost increases considerably. The first one requires only a 100 Rupees, the second 500, the third 1000, and the fourth... 10,000 Rupees! The silver lining is that when you free them, you don't have to pay for the upgrade. Remember, though, that each upgrade also requires a certain amount of materials and other items.
Below you can find an index of every fairy in the game - the order in which you visit them does not matter.
Cotere is nearby Kakariko Village. If you talk to the village dwellers, they will tell you of a fairy that lives near the shrine in the mountains.
Kayasa resides in the very center of the Great Fairy Fountain. She's very close to the Dah Hesho Shrine - from the shrine, you can glide straight to the fairy.
It's easy to reach her by gliding from the Tabantha Tower. Just look for a big flower when standing on the tower and glide towards it.
This fairy is definitely the hardest one to find. She's at the very edge of the world, near the Gerudo Great Skeleton. Traveling across the desert will be challenging - make sure you travel at night if you can and wear light clothes.