‘bring him down’ with the meaning you’re asking about needs to be followed with some kind of measure (a notch, a peg, a bit …)
His string of wins has made him insufferable. I’m hoping for a loss that will bring him down a notch.
This defeat will bring him down a peg or two, but I don’t think he’s capable of humility.
By itself, without a measure, you’d typically be talking about someone’s actual defeat, not their attitude.
The massive riots brought down the government.
Many tried, but nobody was able to bring him down. He retired undefeated.