If you want to find all of the items for the Collector and discover many more secrets in Dredge, then you're going to need some explosives. The quest to obtain them can be found in the Gale Cliffs, which I'd advise against heading to before you've upgraded your engine, added on at least one other light, and found the Ornate Key for the Collector that will grant you the Haste speed ability. You'll also need the Dredge ability from the Collector if you haven't spoken to him yet.
If you want to upgrade your hull you'll need refined metal and if you want to reduce your chances of depleting fishing stock, then you'll want to find the Stoplight Loosejaw. With all that in mind, here's how to get your hands on some explosives.
How to get explosives in Dredge
Once you've reached the Gale Cliffs, you'll want to find the Hermit in the ruins near the island of Ingfell, in the northwest of the region. You'll also want to talk to the Retired Whaler on Ingfell, who is the Hermit's brother. Essentially, you'll need to find the Family Crest to reunite the brothers. As ever, watch out for that giant fish that likes to come and bash your boat in the night.
In the southwest of the region, in an open area, you'll find the Family Crest. There's a nameless dock to the south, so go around the island to find the entrance to the area. You'll spot the dredging point by its golden glow and, after a few moments, you'll find the Family Crest. Once you've got the crest, head back to the whaler and he'll ask you to blow up the target wall—he's already set the explosives up. Head through the archway in the rocks and look for the wall littered with yellow flags, as you can see below.
Interact with the wall to blow it up and, once again, watch out for the large boi under the water's surface who will come and attack you if you don't sail away fast enough. Speak to the whaler again then head over to get the hermit, then you'll receive the explosives. The explosives are single-use and take up cargo space, and you'll be able to buy them from him and other merchants for $40 at a time. You can keep them in your storage, too. You can find the Dusty Pontoon merchant in the Gale Cliffs area too, so be sure to buy the Refined Metal while you're here.
If you sail back to the ruins and blow up the wall, you'll find the Rusted Music Box for the Collector, too.