Achilles is a mythical character who was very commonly mentioned by Dee Dee in Big Nate Goes For Broke. Nate did not know who he was until Ellen Wright shows him her essay about Achilles.
In greek mythology, Achilles what dipped into the River Styx by Peleus so he would be indestructible, not realizing that his heel never touched the water. During the Trojan War, thousands of trojan arrows struck Achilles but had no effect. But then, one arrow hit him in the heel (the vulnerable part of his body). Because of that, Achilles died.