Nemesis, say (3)
(Other definitions for foe that I've seen before include "opposing side" , "Someone opposing" , "friend never!" , "Antagonist" , "Adversary" .)
(Other definitions for rival that I've seen before include "Competing opponent" , "Someone you hope to defeat" , "Person in direct competition" , "Contestant you hope to defeat" , "Be equal to in quality" .)