There are 10 alpha (legendary) animals to find throughout Valhalla.
Legendary animals appear as a paw shaped mystery icon when found on your map. They are often levelled around 300 and can be more challenging than your regular enemy. Writing this, I am level 241 and successfully won all fights.
As far as inventory preference goes, I'd recommend using whatever you're comfortable with and have upgraded. I was using Mournful Cry as a weapon which can be purchased from Reda's shop after speaking to Randvi and Ceolbert in the Ledecestrescire settlement. The weapon has a decent attack at 129 as well as fair speed at 50. Daggers or Excalibur are also good alternatives and always favour evacive gear.
Locations and where to find them:
Alpha Animal #1: Elk of Bloody Peaks - Rygjafylke.
Alpha Animal #2: Bear of the Blue Waters - Hordafylke
Alpha Animal #3: Black Shuck - East Anglia
Alpha Animal #4: The Corpse Feeders - Oxenefordscire
Alpha Animal #5: Beast of the Hills - Sciropescire
The beast is accessed via Uriconium Mines.
Alpha Animal #6: Gemad-Wulf - Lincolnscire
Alpha Animal #7: Aelfred’s Battle-Sow - Suthsexe
Alpha Animal #8: The Blood Swine - Eurviscire
Alpha Animal #9: Elder Lynx & Young Lynx - Hamtunscire
Alpha Animal #10: O Yan Do’ Ne - Vinland