After defeating Eckhardt, as shown in the previous section, you must now beat Karel (4). Since he's an actual angel, he cannot be killed directly. You'll have to make your way up to the suspended Sleeper to set things in motion. First run or crawl to Eckhardt's body. (Karel's green energy bolts will rarely hit Lara if she's crawling.) Pick up ECKHARDT'S GLOVE (7).
When you do, your notebook is updated (62/62): "Use the Glove to destroy The Sleeper." (Again, this page on Von Croy's Notebook lists all entries.)
NOTE: If you have collected and read all 62 notebook entries, the "Memento Mori" achievement/trophy should unlock here. If you have 62, but the achievement doesn't pop, you probably just forgot to examine one of them. Try paging through all of the entries, and it should happen.
Now head for the pillar to the left of the one supporting Eckhardt's body.
On the back of this pillar is a control panel. Press Action to use ECKHARDT'S GLOVE to lower a pair of ladders.
Run or crawl to the nearer of the two ladders (just to the left of the control panel) and climb to the first-level walkway surrounding the arena.
At the top of the ladder, turn left and follow the walkway to another ladder leading up to the next level. Again, you can run or sprint to avoid Karel's blasts. Or, if you're very low on health, commando crawl to avoid taking damage. Climb to the second level.
The second-level walkway has a wide gap to the right. You can make it across using a sprinting jump, but if you try and do a regular running jump and grab, Karel will probably zap Lara, causing her to fall before she can pull up. You may be better off running (or crawling) around the long way, to the left, to reach the opposite end.
The ladder from the second to the third level is on the back of the support column just beyond Eckhardt's pentagram-inscribed control panel. Climb up.
On the third level, either take a carefully angled running jump across the wide gap on the right, risking a fall if Karel hits Lara with an energy bolt. Or, run/crawl the long way around to the left...
...to where the walkway juts out toward The Sleeper. Take a running jump toward it to trigger the final cutscenes. (These are detailed in the main walkthrough.)
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