As well as the nine Dreadnaught chests that need specific keys before they'll pop open, there are two chests aboard the ship that require more unorthodox methods to unlock. You'll find Calcified Fragments in both as well as some other bits of loot.
A Scent is the Key
In the Mausoleum, head through the doorway along the left wall that's to the left of the pointed one.
Go on through the tunnel in here.
You'll pop out into a cave. If you stay in here long enough, you'll become engulfed in a cloud of green tendrils. Wait for the notification that you've caught the Scent of the Worm. You now have one minute to reach the chest.
If you have a friend or two with you, get them to stand on the invisible platforms that line the route, and run ahead of you, so that you don't have to waste precious seconds whipping out your Ghost to see them. If not, a practice run might be useful. Head to the right side of the Mausoleum and follow the walkway to the circular platform at the end.
Drop down onto the ledge to the right and hop over to the first invisible platform.
Head left where the path forks.
Jump over to the platform ahead.
Head left again.
There are two more platforms ahead of you before you reach the large one on the left wall.
When you land, a few invincible Blind Thrall will emerge from the pools here, but as long as carry the scent, they'll ignore you.
The chest is at the far end to the left. It takes a while to open and if you lose the scent while you're waiting, it's back to the stinky cave for you to wait for another run at it.
Hang around the caverns near the Court of Oryx in the Hall of Souls until you hear the Hive praying, then start killing them.
Pick off the Hive and Taken, and soon after, a yellow miniboss will appear. Defeat him and be sure to mop up any stragglers.
When the area has been cleared, a notification will tell you that a relic is being pulled from the void. The orb will spawn in the mechanism above. There are a couple of them in the adjoining caverns, so if it's not materialising in front of you, have a peep in the next cave over.
Pick up the orb and make your way to the area of the Hall of Souls that leads to the Hull Breach, To the left of the main doorway leaving the area, is a smaller door that you need to head through. There's a timer on the orb but you should have plenty of time to make it to the chest.
Go through the tunnel to the right.
In the next room, go past the Key of Akka chest on the right and head through the tunnel ahead.
At the fork, go right.
The Taken Consumption chest is in the cave at the end.
This chest also takes a while to open but as long as you're holding the relic, you'll be fine. The alternative method to open this chest is to use a super just outside and run in to open the chest. You'll most likely die just as it opens, but you'll still get the loot. Use either the Hunter's Blade Dancer, the Warlock's Sunsinger, or the Titan's Ward Shield.