Open the Messages app
Select the conversation or message thread
Delete the message or conversation
Empty the Recently Deleted folder if available
Turn off message syncing on other devices
Delete backups that contain the messages
Disable cloud backup before deleting if needed
Sign out of synced accounts if messages are stored there
Ask the recipient to delete their copy
Contact your carrier if message logs are stored there
Use a secure erase tool for the device if you want a full wipe