Yep, I had the same issue. Incredibly frustrating part that doesn't telegraph what it wants you to do very well.
You need to use the mirror on the black goo until it's roughly a quarter or so left? At that point jump onto the cage and climb up. You'd think it wants you to make it recede entirely but nope.
It attacking you when you do that isn't enough of a clue? Does it have to outright kill you for you to get that you shouldn't be doing that?