While the goal of exploring the Bone Vaults is just on the other side of the whale skeleton to your right, your path lies to the left.
Sonar blast your way through the glass gate you see there.
The red lever you see will turn on a beam grid that will probably be useful later. Leave it off for now.
Head down and to the right. Let the currents carry you to the magma and ice walls.
Blast your way through and head up.
Follow the path around and make your way through the smashing pillars.
Use your fancy new Full-Spectrum Search Lights to make the trip up through the anemones much easier and pass through the gate.
Work your way through the annoying pillars and keep following the path to the Tyne Wellspring and Seahorse Parts.
As soon as you grab the Seahorse Parts, you will be pursued by Red Reapers. This will take several tries, so make sure you hit the Tyne Wellspring on your way back past to ensure you start with the parts and a modest head start on the reapers.
There are no treasures or secrets in this area. Your job is to rush back through the tunnel to that beam grid at the very beginning without getting caught by the reapers.
After you do that seven or 20 times until you get it exactly right, head back to the Tyne Wellspring.
Head straight up along the dark passage back to The Maw. Again, use your sonar and take it slow to avoid the Reapers. Keep to the right side as you exit the darkness and keep going up past the Tyne Wellspring.
Fight your way through the enemies, then use your searchlights to claim a gem worth 200 coins that's hidden in an anemone.
Keep going up until you see the Tyne Wellspring and Tyne Vortex. Take the Vortex to The Skeleton Reef.