Set Instant Pot to the Saute function and add 1 Tbsp oil to the insert.
Season steak chunks with salt and pepper. Once the oil is hot and shimmering, add steak and sear on all sides. This will take about 5 to 6 minutes total. Remove steak to a plate.
Add in remaining Tbsp oil and onion. Saute, stirring occaionally, until softened, about 3 to 4 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Turn off Instant Pot.
Stir in chicken stock, beer, and lime juice. Use a wooden spoon with a flat edge to scrape the bottom of the insert well. Make sure you scrape up any browned bits that got stuck!
Stir in all remaining ingredients and add the meat back to the mixture, nestling the chunks into the soup.
Seal, set to Manual and cook on High pressure for 30 minutes. Let naturally release pressure for 10 minutes, then manually release any remaining pressure.
Remove the chunks of meat to a cutting board and shred using two forks. Return the shredded meat to the soup, stirring well to combine.
Serve immediately with your favorite toppings!