Legolas has no fear whatsoever of ghosts of Men

‘My blood runs chill,’ said Gimli, but the others were silent, and his voice fell dead on the dank fir-needles at his feet. The horses would not pass the threatening stone, until the riders dismounted and led them about. And so they came at last deep into the glen; and there stood a sheer wall of rock, and in the wall the Dark Door gaped before them like the mouth of night. Signs and figures were carved above its wide arch too dim to read, and fear flowed from it like a grey vapour.

The Company halted, and there was not a heart among them that did not quail, unless it were the heart of Legolas of the Elves, for whom the ghosts of Men have no terror.

‘This is an evil door,’ said Halbarad, ‘and my death lies beyond it. I will dare to pass it nonetheless; but no horse will enter.’

‘But we must go in, and therefore the horses must go too,’ said Aragorn. ‘For if ever we come through this darkness, many leagues lie beyond, and every hour that is lost there will bring the triumph of Sauron nearer. Follow me!’

Then Aragorn led the way, and such was the strength of his will in that hour that all the Dúnedain and their horses followed him. And indeed the love that the horses of the Rangers bore for their riders was so great that they were willing to face even the terror of the Door, if their masters’ hearts were steady as they walked beside them. But Arod, the horse of Rohan, refused the way, and he stood sweating and trembling in a fear that was grievous to see. Then Legolas laid his hands on his eyes and sang some words that went soft in the gloom, until he suffered himself to be led, and Legolas passed in. And there stood Gimli the Dwarf left all alone.

His knees shook, and he was wroth with himself. ‘Here is a thing unheard of!’ he said. ‘An Elf will go underground and a Dwarf dare not!’ With that he plunged in. But it seemed to him that he dragged his feet like lead over the threshold; and at once a blindness came upon him, even upon Gimli Glóin’s son who had walked unafraid in many deep places of the world.

The Return of the King, Book Five, Chapter 2: The Passing of the Grey Company.