Encounter That Offers a Chance to Find a Quest Battle/Animal

Hi there! I don't know about you, but the "battle 3 of ___" quests are the bane of my existence. I seem to run into horrendous luck again and again- particularly when it comes to mustelids, marine animals, and bears! I'm currently stuck on the mustelid one, and I suppose the fear of expiration is what inspired this idea. So then! I propose:

An encounter that offers a chance to find the respective animal/battle encounter needed for a quest.

Think of the snake encounter which gives you the chance to find items needed for a quest, but with a battle instead! Something like, "The bushes seem to be rustling behind you. Do you give them a look or carry on?" Giving them a look either triggers a battle with the animal you need, or says something along the lines of, "You look around, but nothing seems to be there. Maybe you were just hearing things?"

I know there have already been talks/suggestions to up the battle quests chances, but I just thought this would be a creative alternative! You of course can still run into the animal in question, but this encounter would provide an additional boost/chance of finding one! 

highly support!