So, I decided to finally challenge myself and attempt to solo the Shattered Throne. I also streamed this for all my friends to see. The entire thing took me under 2 hours to complete, and I started soloed the entire dungeon from start to end as you see from the VOD from my stream. the issue is even after me trying and succeeding I never got the emblem nor the triumph completed for soloing the Shattered Throne. I have a pretty good idea of why it didn't complete. I helped my friends get the eggs and bones in the shattered throne and I missed the ones in the beginning. so I loaded back in to get the beginning eggs without completing the first encounter. I also noticed when I started my run I started really close to the first encounter but thought nothing of it until I finished. If the reason I didn't get my emblem or the Solo-Nely triumph completed was because I didn't walk to the first set of doors to get to the first encounter on my own, that's kind of silly in my opinion. I just find it super demoralizing to try a hard activity by yourself and not get rewarded for your triumphs. I don't expect this issue to be resolved but I do want to bring this to Bungie's and other's attention. so you don't get scolded like I did.
It won't count unless you do a 100% run. You have to start from the initial long passage, up to the doors that lead to the first encounter. If you had already gone in and it caused you to start anywhere other than that very first spawn point, that why it didn't work.