The Leviathan Axe is the default weapon that Kratos will be equipped with alongside his shield at the beginning of the game. For this trophy, you will need to upgrade the Leviathan Axe to level six at any shop in the game. Materials known as "Frozen Flames" are required to upgrade the Leviathan Axe, and they are dropped from main story bosses, so they cannot be missed. If you were to forget to pick up one, you can always retrieve it by going to the "Lost Items" section in any of the shops.

Once you've completed the main story, you'll only be able to upgrade the Leviathan Axe to level five at the highest by using the Frozen Flames you've gained. To reach the highest level, level six, you will need a rare material called a "Chilling Mist of Niflheim", and it can only be obtained by opening the chests at the Workshop's central chamber in Niflheim (see  Darkness and Fog for more information).

Once you have opened enough of the central chamber chests and earned the Chilling Mist of Niflheim, you will need to return to either Brok or Sindri and go to the "Buy" section. Under that select "Resources", and from there you will be able to trade in your Chilling Mist of Niflheim for one more Frozen Flame, which will allow you to fully upgrade the Leviathan Axe.