Oke so first off, this isn't really a solution on how to get the achievement, but more to help people for whom the achievement refuses to unlock (like myself).
If you want to know where the 15 Island Events are just look at Spilner's solution, he has posted an excellent map for all 15 of them.
For me the achievement didn't unlock although the progression within the game stated that I found all 15 events. I first tried to unlock it by finishing all 15 events, without result. So, it seemed that I would have to start over from scratch and lose all my progress, something I didn't wanted to do.
So, here's what I did to get the achievement without losing all my progress.
First of you need 2 consoles (Xbox One, Xbox One X, Series S and/or Series X). I myself used my Series X and my Xbox One. My Series X (first/backup console) contained the progress that I wanted to keep, the Xbox One (second console) I used to unlock the achievement.
- On your second console, on the Burnout Paradise Remastered tile press
and go to "Manage game and add-ons". - Go to "Saved data" and delete you "Saved data" by going to: "DELETE FROM CONSOLE".
- Now disconnect your console from the Internet by unplugging the network cable. Maybe you can go to Settings and select "Go offline" but I'm not sure if that works (leave a comment if you tested it and it works or not). Note: Launching the game while still connected to the internet and cancelling the Syncing process doesn't seem to work. At least for me it didn't.
- While disconnected from the internet start up the game and if all went well you will have to accept the UELA/Legal Terms again. Meaning you have started a new game.
- After the Intro/Tutorial go to Big Surf Island and find 14 of the 15 Island Events.
- Plug your network cable back into your Console and go to the 15th event. As soon as you have found it you should see an onscreen notification and a few seconds later the achievement should unlock (it did for me).
- Dashboard and Quiet the game, go to your "Save data" and delete it (again by using: "DELETE FROM CONSOLE").
- After that start up the game again and it should start with Syncing your Save data. When the game has launched you should continue with your original progress.
I hope this will help you with unlocking the achievement without losing all your progress within the game.
Note: I haven't tested the following, so I can't guarantee that it works this way. Try it at your own risk.If for some reason you are still in your 'new' game, you could go to your Save data and use the "DELETE EVERYWHERE" option. According to the description this should deleted the data from you console and the Xbox Network, but not from the "First/Backup Console". So if you start the game up again on your first/backup console you should be able to continue with all your progress and when your done playing, it should sync with the Xbox Network again. Or maybe start the game up while being disconnected on your First/Backup console and only reconnect while in the game is running to be save.