Aragorn goes to Boromir and hears his dying confession:
"I tried to take the Ring from Frodo," he said. "I am sorry. I have paid..."
Hearing this, Aragorn offers absolution:
"No!" said Aragorn, taking his hand and kissing his brow. "You have conquered. Few have gained such a victory. Be at peace!..."
But how has Boromir conquered? He clearly lost the fight with the orcs, the hobbits captured and himself mortally wounded. Are Aragorn's words a comforting lie to console a dying man?
Interpretations may abound here, but I think Tolkien intends us to see victory in Boromir's confession and repentance. I think the drama of the story makes it clear that after Boromir stumbles badly with Frodo, he finds himself again in loving sacrifice, in giving his life away to save others. In taking that moral journey, from grasping at power to sacrifice, Boromir finds his way back into the light. This is his victory.