Mythic rare cards (or spells) are the rarest in the game, and can be easily recognized by their bronze colored set symbol (the D13 under the card's art). For example, Celestial Light, has two mythic rares; "Baneslayer Angel", and "Felidar Sovereign". Each deck has its own mythic rares.
The quickest deck to unlock mythic rares for is Talrand's flying "Crosswinds" deck. Complete four games and you will unlock your first mythic rare. Place that into your deck, play enough lands and then cast one of these in any game mode and the achievement will unlock. A full list of mythic rare cards can be found here.