Keep going down and follow the path to the right. Hop into the current and let it push you down.
The room below is filled with underwater spider webs. Watch for the sacs that you can break for some easy coins.
Head left, past the fisherman's glove and then go down to the next wellspring.
Make sure you save here. In fact, if you have the coins, it's probably worth the long trip back to the top left corner of Skeleton Reef to visit the hermit crab and upgrade your sub. You should have the coins to buy either the claw or the boost upgrades. We went with the Double Turbine upgrade to help deal with the currents and because you're about to get a weapon upgrade anyway.
If you took our advice and bought the boost upgrade, take a quick detour back up from the Watcher wellspring. The new Double Turbine should let you push you way through to the room above the current. Pull open the chest for a Hull Fragment to upgrade your health.
Saving and upgrading are important here because you're about to fight the eponymous Watcher, whose appearance finally explains those underwater spiderwebs (hint/spoiler alert/trigger warning: it's a spider).
The Watcher appears far more dangerous that it actually is. You have two priorities during this fight: avoid getting hit by enemies (and later the acid the Watcher spits) and remove the webs holding up the shipwreck. Beyond that, you should try to avoid getting snagged and cocooned, but even if you do get caught, it causes no damage and you can break out pretty quickly just by firing your claw.
Your first target is the cocoon that lands in the web. Destroy it and The Watcher will come investigate. Use this distraction to skirt around it and grapple one of the webs up top. Use your boost to pull it free, then retreat to the bottom of the screen. If you can't get it free or you get caught, just head down to the bottom of the screen and try again.
Pulling the first web free will trigger some nettles to spawn. Take care of them, then repeat the same process with the cocoon and the web.
Repeat the investigate-break-retreat-kill enemies process a couple more times. Try to keep track of which side you're pulling from so you don't waste time on a side you're already cleared.
After you pull three of the webs free, the Watcher adds a new twist and fires green acid/venom at you.
Conveniently, it also fires the occasional ball of webbing. Grab these, like in the image above, and fire them to cover the Watcher's eyes.
Just keep pulling down webs and avoiding spit and enemies a few more times. Then there's a crash, cue the Game of Thrones reference and you're victorious.
Head up above to investigate the cocoon Merryn noticed earlier.
Sadly, it's not her father, but it is a new friend named Swish.
Follow him straight down where he'll retrieve you a weapons upgrade, Tyne Torpedoes.
You can immediately use your new torpedoes to blow up a gate to your right and gain access to a new section of the Undying Caves.