If you are hunting a Fallen Boss for the Rasputin Fallen Sword bounty, you have a couple of options available without needing to tie yourself up in a Strike.
Fallen Public Events, which take place on Earth and Nessus a lot, are a great place to find a Fallen Boss. They are generally pretty quick to complete. If you are doing the Glimmer Extraction, you will need to make the event Heroic by killing the small machines that spawn in on each wave to get a boss to spawn at the end. If you are doing the Ether Resupply with the giant Servitor enemy, then you can kill them without making it Heroic.
Ether Resupply will take place at Watcher’s Grave and Exodus Black on Nessus, and the Outskirts and Firebase Hades on the EDZ.
Glimmer Extraction will take place at Trostland, The Sludge, The Gulch, and Firebase Hades on the EDZ, and the Tangle, the Cistern, and the Glade of Echoes on Nessus.
If you wish to use your time efficiently, you can try the new Seraph Tower event near the Winding Cove in the EDZ. This will throw waves of Fallen at you, including some Fallen Bosses for you to kill.
K1 Logistics on the Moon
The K1 Logistic Lost Sector on the moon houses a Servitor at the end that will also count as a Fallen Boss. It’s unusual because these enemies are normally coded as a vehicle, but this one will count for this bounty.
Just make your way to the area shown in the video above, then fight your way inside. You will need to clear each section before the energy shields drop and allow you to progress. When you get to the end, you will find the Servitor with some small friends. Take out all the smaller enemies, then the Shanks that spawn in, and you will be able to damage the Servitor.
Take him out, and the Fallen Sword bounty will be completed.