Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Melt butter in the pot. Meanwhile, season chicken with garlic powder, salt, pepper, and paprika. Quickly brown each chicken breast in the pot, rotating until browned on all sides, 5 to 7 minutes. Add onions and cook 5 minutes. Add broth, radishes, and garlic.

Change pressure cooker setting to Manual and cook chicken until no longer pink in the center and juices run clear, about 15 minutes.