Some cards (such as Wandering Monster) allow your rivals to send other monsters to join the fight. You must defeat their combined combat strengths.
Any special abilities, such as forcing you to fight with your Level only, apply to the entire fight.
If you have the right cards, you can eliminate one monster from the combat and fight the other(s) normally, but you cannot choose to fight one and Run Away from the other(s).
If you eliminate one monster, but then run from the other(s), you don’t get any levels or Treasure!