The pillager raid achievement will not activate when triggering a raid. I have killed the pillager captain and I become marked with the omen and then go to a village to trigger the raid. I have successfully completed all raids and no achievement at all. I have done this on a friend's world as well as my own realm that I own with a friend and nothing.
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Thanks for your report! However, this issue has already been reported (MCPE-45060.) If you have anything to add to the conversation comment there. Also, please search for an issue before making a ticket. Have a great day! 🙂