Set the Instant Pot to the "Sauté" setting. Pour in olive oil and chopped onions. Sauté for 3 to 4 minutes, until lightly browned.
Add the rest of the soup ingredients (except for the bay leaves) and stir. Place the bay leaves on the very top of the soup.
Lock the lid in place, move the steam release handle to "sealing", and set the Instant Pot to pressure cook on the manual high setting for 10 minutes. (Note: It will take several minutes to build pressure)
When done, let the pressure naturally release for 10 minutes and then manually release the rest of the pressure with the steam release handle.
Carefully, remove the lid and remove bay leaves.
Remove the chicken breasts, cut into thirds, and place in a large bowl. Shred chicken with an electric handheld mixer on low speed.
Place shredded chicken back in the soup and stir.
To make the tortilla strips, place corn tortillas on a baking sheet lined with parchment paper, lightly coat tortillas with olive oil, and cut into ½" wide strips with a pizza cutter. Bake at 350°F for 15 minutes.
Garnish tortilla soup with cheese, tortilla strips, sliced avocado, sour cream, and cilantro.