It's on death battles fanon wiki, here' my commentary.
"It was Eragon's turn to be..."
Highly intriguing and interesting defense against Eragon's mental powers. While Percy is untrained, it's certainly viable that his water powers will indirectly shield his mind because of the concentration it requires to control water.
"Percy was getting fru..."
Haha XD Eragon isn't a head-on fighter like Percy, he's very cautious and prefers to avoid head-to-head confrontation.
"On my word as a Rider..."
Nice by Eragon. Percy doesn't know that he has wards to protect him from physical damage already there, so he isn't breaking his word.
Whether Percy is physically stronger than Eragon is debatable. He's been inconsistent throughout the series. However, Eragon is undoubtedly more disciplined and his swordfights have been more strenous. As for the Ares duel, it's not an adequate measure of Percy's fencing skills.
"Percy knew the..."
and the turning point. Percy thinks that Eragon has broken his promise, so he goes for water.
And Eragon finally abandons restraint and goes for the death words.
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Ultimately, the instant Eragon decided to use magic against Percy, it's over. Even if the death words and direct magical attacks don't work, Eragon can use too many attacks.
Eragon's magic is too versatile for Percy too handle.