As other posters have said, this needs to be flagged as bugged/missable until Playground issues a fix. If you have the seasonal objective complete when a new week starts, you will not receive the achievement and no amount of beating your personal best will pop it. You have two options:
1. Save Scum (not recommended)
Delete/backup your save file, start fresh, work towards unlocking seasonal events and do it fresh.
2. Time Lord (recommended)
If you're on PC (no way to confirm if this works on Xbox), change your date to the following week and then boot up the game. Seasons are tied to your local date and time, not Playground's servers. Keep going forward until you find a stunt that you haven't fulfilled the seasonal PR objective for. It will be red instead of gold, and has a higher requirement than the 3-star rating. As a safety precaution, make sure your game is in Horizon Solo and isn't attempting to load an online session. I had to go 3 weeks ahead to find an event I hadn't already fulfilled. Once I completed the seasonal objective, the achievement popped immediately. I reverted back to standard time without issue.