Possible Clues:

• Holmes and Moriarty, e.g
• Watch people on the up eclipsing second greatest rivals
• Archenemies (note the last 2 letters of this clue's answer ...)
• Pokémon's Gary and Ash, e.g
• Foes that seem impossible to beat
• Rivals who often win out
• Sworn enemies
• Usually victorious rivals
• You can't beat them
• The Steelers, to the Ravens