Heat Instant Pot on the saute setting for 3-5 minutes to allow to get hot. Add avocado oil, and several chunks of chicken. Don't overcrowd, or the chicken will not brown. Season with salt and pepper, and turn chicken to sear all sides.
Remove browned chicken from the pot, and add more chunks of chicken. Repeat until all chicken is browned.
Turn the Instant Pot off Saute, and set it to Manual for 15 minutes (for breasts). Return all the chicken to the pot, and pour the marinade over the top. Seal the lid, and allow the chicken to pressure cook. Set to Manual for 10 minutes if using chicken thighs.
Preheat oven to Broil (the following steps are optional but help concentrate the flavors and crisp up the edges of the chicken).
Allow the pressure to release through the steam valve, then remove chicken from the pot. Shred the chicken with forks (leave some in chunkier pieces), and place on a large baking tray.
Pour 1/3 of the marinade left in the pot over the chicken, and broil for about 4 minutes.
Flip the chicken over, and add another 1/3 of the marinade.
Serve chicken drizzled with the remaining juice from the pot. Garnish with onions, cilantro, and lime wedges, if desired.