Combine 3 tablespoons olive oil, garlic, cumin, coriander, cilantro, and juice of 1 lime in a gallon-sized resealable plastic bag. Add chicken and marinate for 30 minutes.

Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Heat remaining 1 tablespoon olive oil. Add onion rings and cook until soft and translucent. Add diced tomatoes with liquid. Drain chicken from marinade and add to Instant Pot®. Close and lock the lid.

Select high pressure according to manufacturer's instructions; set timer for 10 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure using the natural-release method according to manufacturer's instructions, for 6 minutes. Release remaining pressure carefully using the quick-release method, about 5 minutes. Unlock and remove the lid. Remove chicken and shred with 2 forks. Return to the Instant Pot® and mix with tomato sauce.

Add chicken mixture to taco shells and add preferred toppings. Slice remaining lime and add lime slices to each taco plate.