Diving
Swim out to the reef from the dive rock with your diving kit, or dive deeper from Captain Brine's submarine on Sundays.
You need all three pieces of diving kit (mask, fins and tank), which Captain Brine gives you, one a Sunday, for helping patch his submarine.
With the kit, swim out from the dive rock on the east beach to the shallows any day the sea isn't rough. On Sundays, diving from the submarine reaches the drop-off and the wreck, where you may meet Purrl.