There are two way to gain purple coins
1) collect them throughout the different island
2) wait for a metor shower at night ( random cycle )
If collecting purple coins can be tricky as they are scattered everywhere but spots around the island that are hidden unless you search every in of the islands you wouldn't collect many
The metor shower been the best method so far but this is random it happens at night time weather changes every 10 to 20 minutes, even when it is night it not guaranteed to happen I would recommend to keep playing and you will encounter one as you progress
A cutscene happen when one is active they will be silver orbs scattered around the island beaming will colour so easy to see , each time you collect one you will spin a mini slot machine
This slot machine is random and gives you random amount of purple coins sometimes if your lucky you can get hundreds of them at a time in my first metor shower I got 750 which was plenty for this achievement but don't stop there more you gain the more time you can fish , and you need the fishing to help you with the game faster that I will create a guide for
Happy hunting good luck