Strengthening Welfare in Marine Settings Act of 2022 or the SWIMS Act of 2022 This bill establishes prohibitions on capturing, importing, exporting, or breeding of orcas, beluga whales, false killer whales, or pilot whales for the purpose of public display. Specifically, the bill prohibits the National Oceanic and Atmospheric Administration from issuing any permit under the Marine Mammal Protection Act of 1972 that authorizes the taking (e.g., capturing) or importation of such orcas or whales for the purpose of public display. The bill further revises the act to make it unlawful to export such orcas or whales, unless they are being transported to marine mammal sanctuaries or for release into the wild. Further, the bill makes it unlawful under the Animal Welfare Act for any person to breed or artificially inseminate such marine mammals for purposes of using their progeny for public display.