List two instances of irony in Battle Royal by Ralph Ellison.

One instance of irony is that the white men believe they've put narrator in a position beneath them because he's inferior to them; in reality, he's using their prejudiced beliefs to rise higher than them and change the system in a way they won't like. This idea comes partially from what his grandfather said to him about their family and how they get by. He said:

"Son, after I'm gone I want you to keep up the good fight. I never told you, but our life is a war and I have been a traitor all my born days, a spy in the enemy's country ever since I give up my gun back in the Reconstruction. Live with your head in the lion's mouth. I want you to overcome 'em with yeses, undermine 'em with grins, agree 'em to death and destruction, let 'em swoller you till they vomit or bust wide open."

The narrator has to keep his head down once he's thrown into the battle royal and put through a series of humiliating events. He even has to correct "social equality" to "social responsibility" in his speech to appease the audience. He does win the opportunity he wanted, however, and the speech he prepared captures the audience enough that they do give him a scholarship. This award puts the narrator on the path to make the world a different place. They're giving someone below them an education and a taller platform to have his voice heard, despite the prejudiced beliefs of society.
Another irony in that the boys in the ring are fighting to get money passionately enough that they turn against the narrator; the reward, however, is as fake as the respect the narrator hopes to win through his speech. When the narrator is facing Tatlock, they have an exchange in the ring, saying:

I whispered, "Fake like I knocked you out, you can have the prize."
"I'll break your behind," he whispered hoarsely.
"For them?"
"For me, sonafabitch!"

Tatlock is trying to win for himself—and does, though not as much, as the narrator offered him to throw the fight. He accepts less to win even though it doesn't win the respect or admiration of the gathered white men. They see the boys as lesser beings to play with. That's what Tatlock and the others were fighting for so passionately: a low payment after being humiliated whether they won or lost. Though they are paid in the end, it's only after the scramble on the electrified floor for the brass coins that they think are the real reward. What they get isn't a reward. It's payment for their services. Their passion to win the fight doesn't determine much except that Tatlock gets $10 instead of $5.