In the film, three pets: two dogs and a cat are traveling in the woods to get back to their owners in the city. During the journey, Sassy the cat gets separated from the two dogs Shadow and Chance and is presumed dead. Shadow and Chance are walking near a mountainside and the mountain lion is stalking them from above. He smackers his lips and follows them.
The mountain lion gets closer to them and Chance spots him while Shadow was underwater looking for fish. Chance yells for Shadow to look but when he does the mountain lion disappears. Chance sees him again a little closer and Chance yells again to Shadow and when Shadow furiously looks, the mountain lion lets out a shriek and the two dogs run away. The mountain lion does not chase them but slowly follows them and smells them. The dogs run into a dead end on a cliff above the river. Shadow sees a long rock atop a boulder which looks like a seesaw, with Chance unwittingly providing Shadow with a plan to get rid of the mountain lion (Chance, believing he was going to die, was actually making final confessions to any bad behavior he did, specifically stealing the TV remote and burying it under the Seavors' see-saw set when Shadow came up with the plan). Shadow runs back to find him and starts barking to get his attention. The mountain lion finds him and a chase is ensued. For an old dog, Shadow outruns the mountain lion and brings him back to the dead end.
Shadow stands by the seesaw and toys with the big cat and hopes to get him on the seesaw. The mountain lion does so and Shadow signals Chance to jump on the other side of the seesaw. Chance gets distracted and the big cat, tired of waiting lets out a loud roar and Chance focuses and jumps. The seesaw catapults the mountain lion over the cliff and into the river below. He survives but realizes he is outmatched and runs off scared and the dogs give out a victory bark, with Chance also yelling that "Dogs rule and Cats drool" (a reversal of Sassy's statement to him before then). What ever happened to the mountain lion is unknown.
Chance's nickname for the Mountain Lion is a reference to the Austrian bodybuilder and actor Arnold Schwarzenegger.