First please make sure you have the latest game updates and the issue still occurs after restarting the app and using fast travel in the game.
A possible solution to try is manually syncing trophies.
More info on how to do that here.
If that does not resolve the issue then a potential workaround is to create a manual save with your current progress, load a backup save and unlock the trophy again, finally, reload the manual save you created.
Marvel’s Spider-Man features automatic backup saves at key points in the story, usually when a mission is completed. If your current game slot is stuck in an unplayable state, you can return to a previous save instead of starting the game over:
- From the Spider-Man main menu, select the game slot where you’re experiencing an issue.
- Instead of choosing Continue, choose Load Game. You will be prompted that loading a game will overwrite your current save. Press X to continue.
- The PlayStation 4 Load Game screen will appear, with a list of your save games as well as backup files.
- Using the date, choose the latest file marked [BACKUP].
- Continue playing the game.
You may lose some side content progress depending on the time between when the save was made and when you experienced an issue.