Tyrdda was described as wise, diplomatic, and generous. The ancient Alamarri word for "axe" was synonymous with "weapon", and so Tyrdda's legend mark of "Bright-Axe" is referring to her weapon, which was a fire staff, as Tyrdda was a mage.
In -620 TE her tribe was living near the present-day Lake Calenhad. Due to her beauty she had many suitors, all of whom she rejected. She did, however, have a lover, who is said to have been a spirit, the Lady of the Skies, in the form of an elf. One of her suitors was a chieftain of a rival tribe by the name of Thelm Gold-Handed.
Thelm merged with tribes that fell on bad times by domesticating its members with luxuries such as fattening food. His numerous warriors were skilled in battle and wielded fire-enchanted swords and dragon scale armours. Whilst he dreamt, demons approached him and filled his head with thoughts of conquering a "golden city" full of treasure lying across the Waking Sea, beyond the Valley of Ferelden. He pushed his tribe to their limits in pursuit of this dream. 
He approached Tyrdda with gifts of gold and silver in exchange for her warriors. Tyrdda's tribe was weak from the winter and Thelm tempted Tyrdda to wed him with stories of the golden city full of food, across the sea. She sought the counsel of her lover, who was not fooled by Thelm's promises. Tyrdda refused her suitor's temptations, and did not agree to an alliance with Thelm's tribe, stating that the Fade lies and its demands can never be satisfied.
Thelm did not take the rejection well and came back adorned in mail for battle, wielding a silver shield and dragonbone sword. A fight broke out between the two leaders. As their warriors cheered as they battled, Thelm still tried to persuade Tyrdda to join him in his quest, promising the warmth of the north, saying that the whispers in his dreams promised him so. Tyrdda scorched his gleaming silver armour with fire and ultimately killed him. A sky burial was thrown for Thelm.
Following the battle, Tyrdda left the comfort of the lowlands of the Fereldan Valley and moved her tribe into the Frostback Mountains. The lack of shelter, strong winds and low temperatures affected her tribe heavily, and so she set camp in a found cave. However, it turned out the cave a was a home to a dragon. No blade could harm the beast, and the tribe couldn't leave the cave because of the weather outside. Tyrdda shouted out to her leaf-eared lover that she gave up power to be with them. As she did, a bolt of lightning from the sky struck the cave and caused a cave-in that killed the dragon.
The tribe ventured deeper into the cave and found dwarves in the Deep Roads, ready for a fight. Tyrdda's lover explained to her that the dwarves were confused to have met Tyrdda's tribe, but that they were also honourable. Tyrdda approached the dwarven leader, a prince by the name of Hendir, and acknowledged that the cave belongs to the dwarves, and proposed trade instead of war, and an alliance, which the dwarves accepted.
In a dream, Tyrdda's lover instructed her to bear a child to continue her tribe, prophesying that one day there would be a descendant of her bloodline named Morrighan'nan who "in strength must shine." Choosing to heed her lover's advice, Tyrdda had Hendir sire a child with her.
Her tribe grew strong and ensured the survival of the Avvar. Thanks to the dwarven trade and prosperity, the Avvar defeated their enemies, be it humans or demons, with diplomacy, magic, and swords.
After appointing her daughter as the new chieftain and gifting her worldly goods to the tribe, Tyrdda was laid to rest in a sky burial, so that she could join her lover once more.
The Inquisition can investigate and retrieve Tyrdda's Staff, and discover that the "axe" in her name meant weapon, and the weapon was a staff. They were surprised to have learn she was a mage. The Inquisition can then share these findings with Stone-Bear Hold, who admit that Tyrdda's status as a mage was no secret to them.
↑Codex entry: Saga of Tyrdda Bright-Axe, Avvar-Mother 4:3 Tyrdda Bright-Axe, Thelm Gold-Handed, battle brought with blade and ax, Thelm in mail and shields of silver, shining sheen to turn attacks. Blade of dragonbone now blooded, warrior throats wrung raw with cheers,