I should know this level backwards. It was one of the hardest to find all the secrets. I went through it many times. However, it's been a long time ...
After you've cleared the main chamber with the crystal pillars, you go around a corner. The guardian is in an alcove on your left and there is a ledge & balustrade to your right. This eventually leads to the big Beast and secret area you describe. As you go around that corner you should see something on the floor, or falling onto the floor, just beyond the Guardian. Some demons are heading for it, hence, "I've got to use that thing before they do". Once you kill them, you should just be able to pick it up. No jumping is required. This gives you the Guardian to take on the Beast.
You see Blood going around the corner in question at the start of his Secrets vid for that level. He must have got the Guardian and then doubled back into the main chamber, probably to put the clip in context.
If you don't see anything obvious as you round the corner then you might have hit a bug. Restart the chapter or last checkpoint. As I say, I can't quite remember the object you have to pick up (some sort of disc rings a bell) but it is fairly obvious and there is definitely no jump required.
Again, if you're still stuck, let me know and I'll reload the game.
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