Season both sides of the chicken breasts with 1 teaspoon kosher salt and the ground black pepper.
Set the Instant Pot to Sauté and heat 1/2 tablespoon of the olive oil until shimmering. Add half the chicken and sear 2–3 minutes per side until browned; do not move the pieces while searing. Remove to a plate.
Add the remaining 1/2 tablespoon olive oil to the Instant Pot. Add the sliced onion, minced garlic, chili powder, and the remaining 1/2 teaspoon kosher salt. Cook, stirring, about 3 minutes until the onion begins to soften.
Turn the Instant Pot off (Cancel). Stir in the chopped chipotle peppers and the can of diced tomatoes with their juices. Return the seared chicken to the pot, arranging the pieces in a single layer if possible, and pour 1/4 cup lime juice over the top.
Lock the lid and cook on Manual/High pressure for 8 minutes. When the cook time ends, vent immediately to release pressure and open the lid when safe.
Remove the chicken to a large bowl or plate. Turn the Instant Pot to Sauté and bring the cooking liquid to a simmer; let it reduce 5–10 minutes, stirring occasionally, until reduced by about half.
While the liquid is reducing, shred the chicken with two forks (or your fingers once cool enough).
Turn the Instant Pot off, return the shredded chicken to the pot, and stir to coat it thoroughly in the reduced sauce.
Make the avocado sauce: in a food processor or blender, combine the avocado, Greek yogurt, 2 tablespoons lime juice, and 1/4 teaspoon kosher salt. Blend until smooth and taste; add more lime juice or salt if desired.
To serve, fill tortillas or taco shells with the shredded chicken, drizzle with avocado sauce, and top with any desired toppings.