To bruise the lemongrass, use the flat side of your knife and firmly push down on the inner stalk until it splits open. Then cut the stalks into 3-inch (7.5-cm) pieces.
Combine all the ingredients except the coconut sugar, lime juice, and cilantro leaves in the Instant Pot®. Lock the lid in place and turn the valve to Sealing. Press the Soup button and set the cook time for 20 minutes at high pressure.
Let the steam release naturally, or for at least 15 minutes, before turning the valve to Venting to quick release any residual steam. Carefully remove the lid and remove and discard the lime leaves, lemongrass, and galangal. Shred the chicken into bite-size pieces using two forks. Add the coconut sugar and lime juice and stir to combine.
To serve, ladle into bowls and top with cilantro, along with lime wedges.