The best way to fish up monsters is to use a lure/bait that won't specifically target any fish in the area that you're fishing. Depending on which area on the isle you're fishing, minnows and sliced sardines both will snag bluetail.

Great Blue is a fantastic site that I've used for quite a while now to determine the best location & bait/lure when wanting to target a specific fish. You can filter by fish, area, or bait/lure, or any combination of the 3. Here's the link for puronorgo isle specifically:

http://www.great-blue.jp/?aid=042&bid=&lng=en

As you can see, there's a lot of different types of fish that can be caught in those waters. Using the lure/bait filter I can see that a fly lure, frog lure, or a lizard lure (I highly doubt you have one of these unless you're a hardcore fisherman) won't target any of the fish in the purgonorgo waters besides items and fish like jellyfish (these will have a (rarely) tag on them, and will very rarely nab your line).

So, my best suggestion is to pick up a fly or frog lure, and head out to the isle during a moon phase that is not full. I typically catch way more fish than monsters during a full moon. With that said, I don't have any experience using a lure/bait that's designed to NOT catch any fish during a full moon, but I know if I have the potential to catch fish they will usually bite the line more often than monsters on a full moon.