I have gotten this part of the quest up to 100% (getting crucible kills with TLW equipped) but it does not complete. On the map the tower has a quest icon above it showing I have something to hand in, but when I get there nothing. Have even tried going back into crucible and letting it drop a few percent, and completing it again.
-
Same for me got to 100% then nothing. Really bad glitch man. The quest is hard enough without this happening.