The Tyrfing (ティルフィング Tirufingu, translated Tyrhung in the Fire Emblem Museum and alternately translated Tailfing in Fire Emblem Treasure) was the sword of the Crusader of Light, Baldur in Fire Emblem: Genealogy of the Holy War. In the game, only characters with major Baldur holy blood can wield it, meaning the only playable characters that can wield it are Sigurd and Seliph.
Tyrfing has 30 might and gives +10 Skill, +10 Speed, and +20 Resistance to its wielder. Because of the huge resistance the Tyrfing provided, as well as its 30 Might, it makes defeating enemy mages much easier, even making it possible to defeat Julius without the use of the Book of Naga. Due to this, Seliph (and to a lesser degree Sigurd) is often regarded as a mage killer when equipped with it.
Tyrfing or Tirfing was a magic sword which figures in a poem from the Poetic Edda called Hervararkvioa, and in Hervarar saga. The name is also used in the saga to denote the Goths and the form Tervingi was actually recorded by Roman sources in the 4th century. It is a cursed sword that eventually leads to the death of the wielder and kin.
It can be noted that the original design of the Tyrfing bears a strong resemblance to the original design of the Falchion.
You cannot get Tyrfing for Seliph if you did not get it for Sigurd. This makes sense because if Sigurd did not get it, he was not carrying it when Arvis killed him.