Once you're done with Calcified Fragments XI, XII, XIII, XIV, XV, XVI, XVII, XVIII, XIX, XX on this page, see:
Calcified Fragment I, II, III, IV, V, VI, VII, VIII, IX, X
Calcified Fragment XXI, XXII, XXIII, XXIV, XXV, XXVI, XXVII, XXVIII, XXIX, XXX
Calcified Fragment XXXI, XXXII, XXXIII, XXXIV, XXXV, XXXVI, XXXVII, XXXVIII
Calcified Fragment XXXIX, XL, XLI, XLII, XLIII, XLIV, XLV, XLVI, XLVII, XLVIII, XLIX, L
Calcified Fragment XI / 11 - Conquerors
From the Court of Oryx (in the Hall of Souls), use the platforms out to your immediate right as stepping stones to the area ahead, where there is a chasm and a seemingly inaccessible ledge high above. Using your Ghost, reveal the invisible platforms to make your way to the right-most upper ledge, where the Fragment is embedded just out of view in the structure sticking out the wall.
Calcified Fragment XII / 12 - Out of the Deep
From the Court of Oryx (in the Hall of Souls) looking out, turn around, and head down the right passage. On the right side you'll see a series of tall, square-shaped pillars. Scale them, and look into the dark and you will see the Fragment, ready for the taking.
Calcified Fragment XIII / 13 - Into the Sky
From the Court of Oryx (in the Hall of Souls) looking out, jump off to the pillar just off the right side. The Fragment is sticking out from the edge.
Calcified Fragment XIV / 14 - 52 and One
Between the Court of Oryx (in the Hall of Souls) and Trenchway is a passage that connects the two areas. From the Court direction, you can take a left to a dead end with fallen pillars, where the Fragment is on the right.
Calcified Fragment XV / 15 - Born as Prey
Between the Court of Oryx (in the Hall of Souls) and Trenchway is a passage that connects the two areas. From the Trenchway, before you crawl left into the wall, the Fragment is on the right side behind some broken pillars.
Calcified Fragment XVI / 16 - The Sword Logic
In the Trenchway, go to where you spawned back in the The Dreadnaught mission when you visited the Dreadnaught for the first time. You'll be on the edge of space, where you can drop down to the left, where the Fragment is embedded.
Calcified Fragment XVII / 17 - The Weakness Verse
In the Trenchway, go to where you spawned back in the The Dreadnaught mission when you visited the Dreadnaught for the first time. At the end of the area in the far right corner is a passage, where the Fragment is at the end.
Calcified Fragment XVIII / 18 - Leviathan Rises
This is only available in the Regicide mission. When you're in the Trenchway, taking the thin bridge over the chasm with a series of wide, circular steps leading to a doorway (which takes you to the Oryx battle), go left, where the Fragment is in the pillar in the corner.
Calcified Fragment XIX / 19 - Crusaders
In the Trenchway, in the giant chasm with the invisible platforms, instead of heading down the passage to the Court of Oryx area, look off to the right, where you can pop your Ghost and find another invisible platform that will take you to a different doorway. Inside here is the Fragment in the corner.
Calcified Fragment XX / 20 - Hive
In the Trenchway, in the giant chasm with the invisible platforms, instead of heading down the passage to the Court of Oryx area, go to the opposite end of this upper ledge (so you are on the opposite side of the passage that takes you down further into the Trenchway), and pop your Ghost, to reveal a series of invisible platforms that take you up. You'll find a room up here, with a Fragment embedded in the left side wall.