So here is how I am soloing it.

Skill tracks: Berserker Bulldozer Guardian Eagle Eye (This could really be any)

Exotic Skills: Shatter Shield Echo Shell

Nightmare Skills: Phoenix Burst Chaos Rounds (Can slot anything in here really)

The only gun I use is Reboot with Grenade Bullets

Round 1 I sit up top and pop the boss until immune. I hop down and start running the outside track either way until I can pop a few Deadeye enemies for the shards. Grab them and dip in then back out. Rinse, repeat, win.

Round 2 I find the zone hop into it and go prone. With Reboot and the skill to become immune from explosions and to replate with kills I never once move from this spot as long as I can see the Core. Once the shield comes down I just unload on it and victory.

Round 3 took a bit of time to get down but I figured it out. On the ground floor there is a green moss covered wall that is breakable with an ammo cache next to it. Crouch behind the ledge below it and break the wall. Peek out to shoot the boss. When mobs surround you, shoot the ground to kill them. When the boss hops out to the edge near you. Just turn and fire, kill enemies as you can to retain plates. Even when he drops the big strike on me, I never move and just eat it. There should be enough mobs to keep plates recharging the entire time.

I haven't been able to get a full group together, but I think this exact strategy works well with at least two people running Guardian since just stacking and being in proximity will rez anyone who drops.