Valthor considers pride in one's own abilities paramount to a champion.
'Your skill in battle cannot be denied, ${PLAYER}.
'The difference between a good champion and a great one is their renown. The peoples of Middle-earth need to know that there are warriors out there capable of incredible martial prowess, risking their lives to fight the enemy.
'For your second task, I want you to travel to Thorin's Hall. Ascend the steps toward Dwalin's throne and proclaim your prowess as a champion to all gathered in the halls of the dwarves!'
Dwalin's throne is in Thorin's Hall, far to the west of Moria.
Valthor has instructed you to go forth and boast of your great deeds before the throne of Dwalin.
Thrymur is near Dwalin's throne in Thorin's Hall.
Thrymur was not impressed with you. You should speak with him again and proclaim your great deeds.
Valthor is at the Shadowed Refuge in Khazad-dûm, far to the east of Thorin's Hall.
Thrymur told you to return to Valthor in Moria and repeat what you said to him.